Babel was apparently the capital city of the kingdom on Nimrod . And they said, Go to, let us build us a city and a tower, whose top may reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth. |
And the Lord said, Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do. |
So the Lord scattered them abroad from thence upon the face of all the earth: and they left off to build the city.  The continents were formed at this time during the time of Peleg and Nimrod. |
Fundamentally, the problem with Nimrod and the people of his kingdom was they completely disconnected themselves from the Lord.
The fact that they undertook such a monumental task upon themselves with no consultation with the Lord, in apparent disregard for Him was the problem.
Their objective was to reach heaven. Now they did not have a clue about the magnitude of the universe, so we should not laugh too loudly at the foolishness of their plan.
Getting to heaven, after all, is what most Christians aspire to. So, their goal, though unreachable, was not apparently in conflict with the purpose of Christ Jesus, our Mighty God and Saviour .
So what specifically was our Lord's problem with their effort? They either had no knowledge of or they did not accept the notion of GodAndMan.
Since Nimrod was the great-grandson of Noah, it is highly unlikely that he had no knowledge of God, no awareness of the cause of The Flood.
So, I can only assume that Nimrod rejected the notion of GodAndMan, preferring to set out to live life his own way. And, as a mighty man who controlled the lives of the people in his kingdom, he directed them to ignore the notion of GodAndMan and serve him in a very Secular Humanism way.
The Tower Of Babel actually happened but it is a metaphor for Secular Humanism teaching us the utter disgust that our Lord has for those who live their lives and teach others in rejection of the notion of GodAndMan.
Although we are in the Age Of Grace and do not see the Wrath Of God being poured out with unilateral action to confound the languages and divide the earth, the End Of The Age is upon us with the Return Of Christ looming in which the Day Of Wrath will be poured out on the Children Of Disobedience.