Well that's the thing. They were good reasons. Bruce firsthand experienced and saw the destruction Supes can cause, and Supes believes everybody, including himself, should have fair judgement by the law, and a vigilante like Bats shouldn't trample on civil liberties to decide justice themselves. Like I said, great themes there. Not to mention, you know, the small fact of Luthor threatening to burn his mom alive.
Better than Ultron wanting to destroy humanity because he spent 2 minutes on the internet.
They stopped because Clark said "HE'LL KILL MARTHA". Hearing a woman is about to be killed who has the same name as your mom who was also killed will obviously get you to pause a minute.