WARNING! Spoilers ahead for Bel-Air episodes 1-3!
Carlton Banks was always Will’s most significant antagonist in Bel-Air. In Fresh Prince, Carlton's character immediately disliked Will, with Carlton disapproving of his immature behavior and, particularly, how Will would undermine his "Blackness" by calling him white. Carlton was much goofier and would be the punchline of Will’s jokes about the difference between his family’s culture in Bel-Air compared to Philadelphia, but Carlton didn’t actively despise or act as rude to Will as he does in Peacock’s Bel-Air.
The most distinct difference between Fresh Prince and Bel-Air's characters is Carlton Banks, who is now popular, a jock, and outwardly confident in his charm. While Carlton was still hesitant about taking in Will in Fresh Prince because he believed Will couldn’t conform to the upper-class sentiments of Bel-Air, the new Carlton’s rejection of Will is based on much deeper resentments. Right off the bat, Carlton antagonizes Will about why he’s in Bel-Air, tells Will he’s being too sensitive when he gets mad about Carlton’s white friends saying the n-word, leaves Will behind before school, and instigates several physical fights with his cousin.
Like the original series, Carlton feels threatened by Will’s presence as his family member within their Bel-Air community. If Bel-Air’s Carlton shares one major motivation with Fresh Prince’s character, it’s that both are preoccupied with preserving their reputations. Carlton likely feels threatened by Bel-Air’s Will Smith in that he could harm his reputation as the most respectable, conservatively behaved, involved, and refined student at Bel-Air Academy. Similar to how Will’s background with legal trouble could harm Uncle Phil’s campaign for District Attorney, Carlton fears Will could upend his reputation at school. Beneath this hatred is also a complex conflict with himself, as Will brings to light Carlton’s own insecurities and struggles with his identity both at home and as a Black man in America.
Carlton also clearly has his own prejudices about Black men in America, which Bel-Air's Will character quickly criticizes. When Will brings up how Carlton wouldn’t stand up to his white friends saying the n-word, Carlton suggests that Will is only saying he’s white because he “enunciates his words.” Will thus threatens Carlton’s identity as a Black man, especially as the most popular Black man at Bel-Air Academy who holds positions over fellow white students as the student class president and lacrosse captain. Carlton’s prejudices also contrast those of his father Phil, who was highly involved in the Black community through his old fraternity and upbringing in North Carolina.
When Will arrives in Bel-Air episode 1, it’s clear that he threatens two of Carlton’s most important relationships: his ex-girlfriend Lisa and Uncle Phillip Banks, with whom Carlton isn’t particularly close. Will quickly establishes a rapport with Lisa, and Carlton gets extremely jealous when he sees the two kissing at a party. Carlton still has feelings for Lisa and wants to get her back, and Will is directly standing in the way of their relationship. Will and Phil can also connect much easier based on their backgrounds and priorities of challenging institutions that systemically oppress Black people, while Carlton is more focused on how to get others to like him or internships that uplift his own reputation with the wider Bel-Air community.
To make it worse, Will and Uncle Phil are shown to have a close and casual relationship where they can connect through their priorities, favorite sports, and communities, which makes Carlton visibly jealous. Carlton’s hatred for Will is finally pushed over the edge in Bel-Air episode 3 when he sees that the entire family has skipped his lacrosse game to watch Will dominate in the basketball game, which digs at his insecurities that Will is the son they want instead. Carlton’s volatile nature is increased by his hidden drug problem and largely unaddressed mental health struggles, with Will’s arrival in Bel-Air being the catalyst for his territorial defense mechanisms coming back to the surface.