The reason your worst enemies might have once been friends is the ‘reaction’ to your ‘betrayal’.
In some cases the ‘betrayal’ might be assumed. In some cases it could be as trivial as not agreeing with the other on some minor point.
The sense of ‘betrayal’ overpowers logic and the new enemy will stop at nothing to ‘pay you back’, as many times as possible.
People do not work off of reality or logic, they operate on feelings and attitudes. Feelings overpower logic.