Short answer
The New Testament Gospels say he did, but Islam teaches that these dated words cannot be his. Matthew has Jesus say that some standing there would not die before they saw the Son of man coming. He says "this generation" would not pass until all these things were fulfilled. He tells the twelve disciples they would not finish the cities of Israel first. Paul, a Christian missionary of the first century, wrote as if he expected to be alive to meet the Lord. All of them died, and nearly two thousand years have passed. The Bible's own test is plain: a prediction that does not come true was not spoken by the Lord. Jesus was a true prophet, so these words, as written, cannot be his. Mark has him say that only the Father knows the hour, and the Qur'an agrees: that knowledge is with Allah (﷾) alone.
Full explanation
What the Gospels have him say
Matthew, Mark and Luke all tie the coming of the Son of man to the lifetime of the people listening. Son of man is the title Jesus uses for himself in the Gospels. They also speak of God's (﷾) kingdom coming with power. Some standing there would not taste death first. And "this generation" would not pass away first. Matthew also says that the twelve would not finish the towns of Israel before he came.
“Verily I say unto you, There be some standing here, which shall not taste of death, till they see the Son of man coming in his kingdom.”
“And he said unto them, Verily I say unto you, That there be some of them that stand here, which shall not taste of death, till they have seen the kingdom of God come with power.”
“Verily I say unto you, This generation shall not pass, till all these things be fulfilled.”
“Verily I say unto you, that this generation shall not pass, till all these things be done.”
“Verily I say unto you, This generation shall not pass away, till all be fulfilled.”
“But when they persecute you in this city, flee ye into another: for verily I say unto you, Ye shall not have gone over the cities of Israel, till the Son of man be come.”
The first Christians expected it too
Paul told the Thessalonians, the Christians of the city of Thessalonica, that "we which are alive" would be caught up to meet the Lord. The letter of James says the Lord's coming draws near. The first letter of Peter says the end of all things is at hand. So the first believers expected the end in their own lifetime, just as the Gospels' words say.
“For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep. For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first: Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.”
“Be ye also patient; stablish your hearts: for the coming of the Lord draweth nigh.”
“But the end of all things is at hand: be ye therefore sober, and watch unto prayer.”
The delay was already a problem
By the time 2 Peter was written, people were asking where the promised coming was. They said "the fathers fell asleep" and all things continued as they were. The letter answers them. It does not claim that the coming had already happened.
“Knowing this first, that there shall come in the last days scoffers, walking after their own lusts, And saying, Where is the promise of his coming? for since the fathers fell asleep, all things continue as they were from the beginning of the creation.”
What scholars conclude
Albert Schweitzer was a German scholar who wrote about Jesus in 1906. Since then, critical scholars have widely agreed that the Gospels present Jesus as expecting the end within his own generation. Critical scholars are those who study the Bible as history. Historians of the church record the long line of dates set for his return that then passed. These scholars read the Gospels as history alone. Muslims also have the Qur'an, which names Jesus a true prophet. So Muslims do not accept that he set a date and missed it.
Argues that the Gospels present Jesus as expecting the end of the age and the coming of the Son of Man very soon, and treats Matthew 10:23 as a promise that was not fulfilled.
Argues that the earliest Gospel traditions present Jesus as a prophet of the end times who expected God's kingdom and the Son of Man to arrive within the lifetime of his own generation, citing Mark 9:1 and Mark 13:30.
A history of Christian end-time expectation from the early church to the late twentieth century, recording the many dates that were set for the end or for Christ's return and then passed.
“He said: "I am indeed a servant of Allah: He hath given me revelation and made me a prophet;”
The Bible's own test
Deuteronomy, the fifth book of the Bible, gives the test of a prophet. If what he says in the Lord's name does not come to pass, the Lord did not speak it. The Qur'an records Jesus saying that he is a servant of Allah (﷾) and a prophet. A true prophet does not set a date and miss it. So the dated prediction as written cannot be his. Muslims do not throw out every Gospel saying. They measure each one by the Qur'an, which confirms the earlier scripture and stands as judge over it. Mark 13:32 passes that test; a deadline that failed does not.
“When a prophet speaketh in the name of the Lord, if the thing follow not, nor come to pass, that is the thing which the Lord hath not spoken, but the prophet hath spoken it presumptuously: thou shalt not be afraid of him.”
“He said: "I am indeed a servant of Allah: He hath given me revelation and made me a prophet;”
“To thee We sent the Scripture in truth, confirming the scripture that came before it, and guarding it in safety: so judge between them by what Allah hath revealed, and follow not their vain desires, diverging from the Truth that hath come to thee. To each among you have we prescribed a law and an open way. If Allah had so willed, He would have made you a single people, but (His plan is) to test you in what He hath given you: so strive as in a race in all virtues. The goal of you all is to Allah; it is He that will show you the truth of the matters in which ye dispute;”
Only God (﷾) knows the Hour
Mark itself has Jesus say that no one knows the day or the hour, not even the Son, but only the Father. The Qur'an gives the Prophet (ﷺ) the same answer to give: the knowledge of the Hour, the Last Day, is with Allah (﷾) alone. Neither a true prophet nor a later preacher can set its date.
“But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.”
“They ask thee about the (final) Hour - when will be its appointed time? Say: "The knowledge thereof is with my Lord (alone): None but He can reveal as to when it will occur. Heavy were its burden through the heavens and the earth. Only, all of a sudden will it come to you." They ask thee as if thou Wert eager in search thereof: Say: "The knowledge thereof is with Allah (alone), but most men know not."”
Verse by verse
Matthew 16:28 — Gospel of Matthew, chapter 16, verse 28
“Verily I say unto you, There be some standing here, which shall not taste of death, till they see the Son of man coming in his kingdom.”
Cited for
Christians read this as fulfilled six days later, at the Transfiguration, when Peter, James and John saw Jesus shining in glory on a mountain.
The response
The verse just before says the Son of man will come in his Father's glory with his angels and reward every man for his works. That is the Last Judgement, not a vision on a mountain. And no one says "some of you will not die first" about something one week away.
Where it lands — The context is the final coming in judgement, and it did not happen in the hearers' lifetime.
Matthew 24:34 — Gospel of Matthew, chapter 24, verse 34
“Verily I say unto you, This generation shall not pass, till all these things be fulfilled.”
Cited for
Christians read "this generation" as the Jewish people, or as whichever generation sees the signs.
The response
Everywhere else in Matthew, "this generation" means the people Jesus was speaking to, as in 23:36. And "all these things" include the Son of man coming on the clouds. They also include the angels gathering the chosen from the four winds.
Where it lands — Matthew's own usage points to Jesus' hearers, and the events promised to them did not happen.
Matthew 10:23 — Gospel of Matthew, chapter 10, verse 23
“But when they persecute you in this city, flee ye into another: for verily I say unto you, Ye shall not have gone over the cities of Israel, till the Son of man be come.”
Cited for
Some Christians read the coming of the Son of man as God's judgement on Jerusalem in 70 CE, the year the Romans destroyed the city.
The response
Matthew uses the same title for the same event. He describes the coming of the Son of man as on the clouds of heaven, seen by all the tribes of the earth (24:30-31). His angels gather the chosen from the four winds. Nothing like that was seen in 70 CE. Paul, writing before then, expected the Lord himself to come down and the living to be caught up to meet him. That did not happen in 70 either.
Where it lands — The promised coming was public and in glory, and it did not happen in 70 CE.
2 Peter 3:8 — Second Epistle of Peter, chapter 3, verse 8
“But, beloved, be not ignorant of this one thing, that one day is with the Lord as a thousand years, and a thousand years as one day.”
Cited for
Christians answer the delay by saying that with the Lord a day is as a thousand years.
The response
Islam agrees that a Day with God (﷾) can be as a thousand years of ours. But this promise was measured by the lives of men: some standing there would not taste death first. God's (﷾) long Day does not keep those men alive.
Where it lands — The promise named a human deadline, and that deadline passed.
Perspectives
Mainstream Christian
Jesus made no mistake. Christians read these sayings as fulfilled in the Transfiguration or in the fall of Jerusalem in 70 CE. Or they read them as speaking of a "generation" other than his hearers.
Matthew 16:28 was fulfilled six days later, when three disciples saw Jesus in glory at the Transfiguration.
Rebuttal
The verse just before speaks of the Son of man coming in his Father's glory with his angels, to reward every man. That is the final judgement, not a vision on a mountain. And no one says "some of you will not die first" about something a week away.
"This generation" means the Jewish people, or the generation that sees the signs, not Jesus' hearers.
Rebuttal
Elsewhere in Matthew, "this generation" means the people Jesus was speaking to, as in 23:36. And "all these things" include the Son of man coming on the clouds, with angels gathering the chosen from the four winds.
The coming in Matthew 10:23 and 24:34 was God's judgement on Jerusalem in 70 CE.
Rebuttal
Matthew describes that coming as on the clouds of heaven, seen by all the tribes of the earth. Nothing like that was seen in 70 CE. Paul, writing before then, expected the Lord himself to come down, and that did not happen either.
With the Lord a day is as a thousand years, so the promise is not late.
Rebuttal
Islam agrees that a Day with God (﷾) can be as a thousand years of ours. But this promise was measured by the lives of men: some standing there would not taste death first. God's (﷾) long Day does not keep those men alive.
The Islamic perspective
Jesus was a true prophet, and a true prophet's words come to pass. The Gospels' dated predictions of his return failed, so, as written, they cannot be his words. Muslims measure the Gospels by the Qur'an. Like Jesus in Mark 13:32, it leaves the time of the Hour with God (﷾) alone.
The Gospels have Jesus promise his coming before some of his hearers died. They have him promise it before "this generation" passed, and before the twelve finished the cities of Israel.
Paul expected that he and some of his readers would still be alive at the Lord's coming.
By Deuteronomy's test, a prediction that does not come to pass was not spoken by the Lord.
Jesus was a true prophet of Allah (﷾), so the failed prediction as written is not his word.
The time of the Hour is known to Allah (﷾) alone.