The beauty of the characters of Game of Thrones is that they are complex and morally ambiguous.

Jaime has good intentions but some of his acts such as pushing off Bran and engaging in incest are not good. But he has reasons to justify them such as his genuine love for Cersei and the safety of their children. We see him as a bad person due to how Ned Stark(who we identified as the hero) reacted to him and his attack on Ned's men. However, he attacked Ned for Tyrion which shows about how much he cares for his little brother, which his father and sister don't. Even the reason for him killing the mad king is justified, since he saved half a million lives, although Ned misjudged him.

I always thought that him being an arrogant prick was a fake front concocted to make everyone feel as though he doesn't care what they think of him. Tywin reads right through him on this.

The main reason we thought Jaime is a bad person is because we didn't know his perspective until he meets with Brienne whose influence brings out his better traits. In conclusion, Jaime has good intentions but Cersei's venomous presence and his love for her makes him do morally questionable things. Jaime's complexity makes him relatable to us and that's what makes him a great character