why do transphobes mention pedophiles/compare them to pedophiles when most trans people (as do most people) hate pedophiles?

I think a lot of it comes from thought correlation traps that people easily fall into. The path goes as such

Guys, going into girls bathrooms are creepy sex perverts. -> Guys pretending to be girls going into girls bathrooms are even creepier sex perverts. -> Pedophiles are the creepiest of sex perverts -> Trans people are creepy pedophiles

It's all baseless assumption and bias, and full of logical fallacy's but an incredibly easy train of thought that follows normalized cultural perceptions for decades. That's why people get stuck on those issues, when it really shouldn't be a big deal at all.