What makes you think that
Apple has a database of actual child sex abuse images? Does that feel like a thing you'd be OK with? "Oh, this is Jim, he's the guy who keeps our archive of sex abuse photographs here at One Infinite Loop" ? If you feel OK with that at Apple, how about at Facebook? Tencent? What about the new ten-person SV start-up would-be Facebook killer whose main founder had a felony conviction in 1996 for violating the Mann Act. Still comfortable?
Far more likely Apple takes a bunch of hashes from a third party in the law enforcement side of things (ie cops) and trust that the third party is definitely giving them hashes to protect against the Very Bad Thing that Apple's customers are worried about.
Whereupon what you're actually trusting isn't Tim Cook, it's a cop. I'm told there are good cops. Maybe all this is done exclusively by good cops. For now.
Now, I don't know about the USA, but around here we don't let cops just snoop about in our stuff, on the off-chance that by doing so they might find kiddie porn. So it should be striking that apparently Apple expects you to be OK with that.