Why was the tower of Babel built?
The tower of Babel was built because the descendants of Noah's sons, within 200 years, fell into total rebellion and ignorance of God's salvation. They tried to make their own way and approach heaven through false worship rather than God's required blood sacrifice.
Les explains that after the flood, Noah and his three sons started over, but within 200 years their offspring were again in total rebellion and in total ignorance of God's offer of salvation. Rather than bringing the blood sacrifice and confessing their sin, they tried to make their own way and approach heaven through their own false worship, and that produced the tower of Babel. Les also places Babel roughly halfway between the flood and Abraham, as part of the 2000 years of human failure before God did something totally different.