Not really all that much biblical support for free will, td1

In any case, I'd probably say not to read too much into the story. All it
really was was a mythological explanation of why there's multiple languages, conceived by a people that didn't believe it could happen naturally and
did believe that god was a complete dick (but should be followed lest you
get dicked by it).
As to the quote:
Now the whole world had one language and a common speech. 2 As people moved eastward,[a] they found a plain in Shinar[b and settled there.
3 They said to each other, “Come, let’s make bricks and bake them thoroughly.” They used brick instead of stone, and tar for mortar. 4 Then they said, “Come, let us build ourselves a city, with a tower that reaches to the heavens, so that we may make a name for ourselves; otherwise we will be scattered over the face of the whole earth.”
5 But the Lord came down to see the city and the tower the people were building. 6 The Lord said, “If as one people speaking the same language they have begun to do this, then nothing they plan to do will be impossible for them. 7 Come, let us go down and confuse their language so they will not understand each other.”
8 So the Lord scattered them from there over all the earth, and they stopped building the city. 9 That is why it was called Babel[c]—because there the Lord confused the language of the whole world. From there the Lord scattered them over the face of the whole earth.
Ninja'd a bit, but whatev'.
The specific line you're looking for is
Then they said, “Come, let us build ourselves a city, with a tower that reaches to the heavens, so that we may make a name for ourselves; otherwise we will be scattered over the face of the whole earth.”
It says it right there -- the reason they were doing it and making a name for themselves was to prevent their people from being scattered across the whole of the earth. It wasn't pride, it wasn't trying to reach the heavens for poke the eye of god or anything like that, it was just so that mankind would maintain solidarity and not become less than they could be.