The official explanation was based on three important points:
1) There would be more casualties for the American soldiers if they continued to push into Baghdad
2) The Bush administration believed that Saddam Hussein would be deposed in a coup after the war.
3) The U.N. coalition support was only for the reversal of the Iraqi invasion of Kuwait and not for the installation of a new Iraqi government
One most important reason though is the fear that if the U.S. government tried to capture Hussein, he could easily escape from Baghdad and go into hiding. The U.S. government would then have a very hard time finding him.