After the flood, Noah lived 350 years, totaling 950 years of life (Genesis 9:29). Noah had three sons—Shem, Ham, and Japheth. Their families grew (Genesis 10:1), and all Noah’s descendants spoke the same language (Genesis 11:1).
Eventually, Noah’s descendants gathered in a plain in the land of Shinar where they decided to build a city with a tower to make a name for themselves and avoid being spread out across the earth (Genesis 11:4). Of course, God was aware of their plans to build the city and saw that nothing they proposed would be impossible for them (Genesis 11:5–6). As a result, God confused the language so that the people weren’t able to understand each other and then scattered them across the face of the earth. The city and tower were left unfinished.
Noah’s descendants were acting in disobedience to what God had told them to do.
Remember that after Noah and his family left the ark, God told them to be fruitful, multiply, populate, and fill the earth abundantly (Genesis 9:1, 9:7)! By building the city and tower of Babel, Noah’s descendants were acting in disobedience to what God had told them to do. They weren’t planning on spreading out and filling the whole earth. They wanted to stay together and “make a name for themselves” in defiance to what God had told them to do (Genesis 11:4). The people of Babel acted selfishly by attempting to do what they wanted to do and not do what God wanted them to do.