I'm always surprised to meet a LeBron fan outside of CLE. There are countless reasons to dislike him:
He's the best. As stated, fans of other teams will always dislike the best. As a Celtics fan, there is no one I have disliked more than his CLE + MIA teams since LBJ entered the league. They were usually the biggest obstacle to a Finals appearance.
The Decision. I've seen some argue that he was young and misguided by his inner circle. But at 25, I think most people would have enough sense to know that'd be a poor decision (no pun). Having been televised and glamorized since HS, he had also probably matured (professionally) than most of his same-age peers by that time. More was (rightfully) expected of him.
He whines. As spelled out above, it's obnoxious. Jordan complained to the refs a lot too. But Jordan was a fiery competitor, whereas LBJ represents the 'soft and entitled' era of NBA athletes. To his credit, most of his peers are too,...albeit very wealthy 'small, sweet baked goods.'
His style of play. As stated, he has barreled his way to the basket with a blatant forearm shove more times than any one can count. He gets away with it, though, because he's LBJ. In the same vein, it's irritating to have seen him take 8 steps on his way to a lay-up. Like most superstars, a different set of rules apply to him.
He's arrogant. Every one appreciates confidence (esp in athletes), but no one likes arrogance. I imagine it comes off as odd to people that don't watch him play that often. I think it's pretty obnoxious given how he carries himself on the court at times, and how good he has it... but I can appreciate him using an 'underdog' mentality to motivate himself.
He's not Jordan. The majority of fans I know that were alive to see Jordan in his prime typically don't like the comparisons. LBJ hasn't been as successful, but more, Jordan was the ultimate alpha dog, the most popular athlete on the planet, and a fierce competitor. LBJ plays well to his strengths, but as such, he's not the alpha that Jordan was. It's hard not to compare their Finals records, too -- for Jordan fans, any conversation starts and ends right there.
Relatedly, he started chasing rings very early into his career. Aside from how he did it, his move to MIA caused a lot of people to lose respect for him. This wasn't special treatment, either -- Durant was demonized the exact same way. I also see a major divide in older vs. younger fans here -- the youth love them some LBJ, while fans that have been around longer seem to think this represented a lack of competitiveness. Maybe worse, it reflected the lack of loyalty in the NBA today.
He's not really human. His lack of injuries doesn't add up, and his physical make-up screams PEDs. I'm not accusing, and I doubt he will ever be discovered a user, but it's not hard to see why people would come to that conclusion... especially if they already dislike him. His hairline also falls in this category: No man has ever demonstrated a severely receding hairline actually reverse its course. The youth find optimism here, while the old grit their teeth in disgust.
He has a history of failing to take responsibility for his teams' shortcomings. Even worse, he has openly throw his teammates under the bus to the media. This ties into his dominant role over the organization he 'plays' for. With Kyrie wanting out, I think most assume that playing with LBJ is not a pleasant experience outside of all the wins.