The internet hating on Wil Wheaton / Wesley Crusher is such an old bit that it has its own momentum and is no longer rooted in anything. Picard yelling “shut up Wesley” is such a meme that people shout this at Mr. Wheaton in public. He’s written about it a lot.

But it is also true that his character was an odd fit: very on-again / off-again as a member of the cast, poorly costumed, and deliberately written as a kind of whiny genius-boy who gets in trouble but always saves the day. Some people found this one of the less enjoyable parts of the show.