I think the idea that it is impossible to know is a little simplistic. And while many people falsely thought the end was nigh, there will be a generation around when Jesus returns. So can we know anything about the timing? And what did Jesus actually say?
On 2 occasions Jesus mentioned to the disciples that they are not to know the time of the end. The first during the Olivet discourse recounted by Matthew and Mark
But concerning that day and hour no one knows, not even the angels of heaven, nor the Son, but the Father only. (Matthew 24:36)The second before his ascension.
But concerning that day or that hour no one knows, not even the angels in heaven, nor the Son, but only the Father. (Mark 13:32)
So when they had come together, they asked him, “Lord, will you at this time restore the kingdom to Israel?” He said to them, “It is not for you to know times or seasons that the Father has fixed by his own authority. But you will receive power when the Holy Spirit has come upon you, and you will be my witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth.” (Acts 1:6-8)During the Olivet discourse Jesus prophesies concerning the destruction of the temple, the distress to come, and his return. It is his return which occasions the comments above. There will be signs in the sky at his return but people will be continuing their usual living: eating and drinking, marrying and giving in marriage; as in the days of Noah just before judgment.
Jesus' comments are notable for 2 things here. Firstly he mentions the day and the hour which may indicate quite a specific time. While not necessarily as specific as a certain day—it could preclude prediction of the year—it does not necessarily mean that one cannot know the approximate time. Daniel gives quite an exact prophecy timewise but it was difficult to understand at the time and even now continues to evade many commentators. Jesus' words here have been used to dissuade prediction and disparage predictors but he may not be completely prohibiting prediction as such. Which brings us to the second notable issue.
Jesus' comments expect men who live in the last days to recognise that they are. Right in the midst of describing his return and warning them that they cannot know the exact time Jesus gives the lesson of the fig tree.
From the fig tree learn its lesson: as soon as its branch becomes tender and puts out its leaves, you know that summer is near. So also, when you see all these things, you know that he is near, at the very gates. Truly, I say to you, this generation will not pass away until all these things take place. Heaven and earth will pass away, but my words will not pass away."When you see what I am describing" says Jesus, "know that my return is near." In fact Jesus' return will be during this generation.
So why have so many people in previous generations been wrong about Jesus' return? It is my contention that there are several conditions given around the end of the world, both here, and in other books such as Daniel, Zechariah, Thessalonians and Revelation. Other generations may have noted aspects of the world that fit some features, but not all. The generation of Jesus' return needs to see all aspects fulfilled, or being fulfilled. Ironically, the failed predictions of previous naysayers may have steeled the last generation against warnings of the end of the world, thus proving Jesus' warning about the days of Noah.
The warning in Acts does not detract from what I have said though it does need commenting on. Firstly, the nature of the kingdom of God was to be different from previous kingdoms of Israel, at least until Jesus' return. Secondly, the disciples concerning themselves with a coming earthly kingdom may have detracted them from Jesus' task which was discipling the world. Thirdly, this was given to the disciples of that time. Now while I think discipling the world applies to subsequent disciples including those of the final generation, this does not preclude the final generation knowing that they live at the time of the end.
In summary, we cannot know the exact time and we should concern ourselves with discipling the world. This does not necessarily preclude knowing the approximate time. And even if we cannot know the approximate time ahead of time, those living in the generation of Jesus' return are expected to be aware that they are living in the last days. Further, they must not be complacent.