it's the same issue as the "black lives matter" / "all lives matter" distinction. On the surface, sure, "all lives matter" sounds more appealing because all lives do matter. But the point is that most people support white people, it's the people of colour that you need to voice your support for, because they're the ones being targeted with constant discrimination and racism.
I think back to the post about liking pancakes not meaning hating waffles. It sounds ridiculous but it's very easy to fall into that mindset, especially in scenarios like this. "I stand with people of colour" doesn't mean "I don't stand with white people", it just means "people of colour need my support more than white people do right now".
If that sounds weird to you still, and you'd still rather say "I support everyone" that's totally fair, but if you're going to do that you need to be aware of the cultural meaning given to those kinds of phrases beyond what the literal words mean, as the type of people who say that sort of thing are usually saying it to delegitimize messages of support for marginalized groups, and so by saying it yourself you may end up being associated with those people as well.
