What does "Boys rule, girls drool," mean? I googled it but did not get a straightforward answer.
It is a dialogue of Dumb And Dumber (2014) film.
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This is an example of "playground language". It is the sort of thing that boys might say on the school playground, when they think no adults can hear them. It is a childish insult.
Saying "something rules" means you think that thing is great. This is a fairly common slang.
I love Game of Thrones. I think it rules.
On the other hand, to "drool" is when spit and saliva drips out of your mouth. You might drool when you see delicious food, but we say that someone who drools all the time must be a dirty and stupid person.
Specifically, the rule/drool pattern (and this use of the word rule in general) was popular among kids sometime around the late 80s or early to mid 90s. I'm not sure if it's entirely gone out of use since then, but it's less common. It wasn't specific to genders but any pair of things perceived as having a rivalry (or rivalry between their fans).
So the whole phrase means "Boys are great! Girls are stupid!" It isn't a very subtle message, but kids love rhyme and kids love being rude.
Adults would never usually say this – unless they were deliberately trying to sound childish for humorous effect. It is sexist and rude. It is in the film as a joke to show that the character is very childish.