If a Pokemon could speak a human language that easily, then wouldn't Trainers such as Ash be trying to do that all the time? Also, Meowth is seen as an oddity, so this isn't an ability typical of Meowth's

My theory? Meowth is the result of a Chatot and a Meowth or Persian breeding. For some reason, the egg managed to hatch instead of ending up as just not happening. So due to this weird combination of genetics, he was able to inherit Chatter, and just didn't figure out how to use it until later in his life

It could also be why his ability to stand and talk causes Meowzie to reject him. She does call him a freak, after all, so maybe she picked up on him being a crossbreed that shouldn't happen

Also note that in Pokemon 2000 he is able to translate what Pikachu and Zapdos are saying to each other, despite it being through electricity. So Meowth's Chatter could have let him figure out what they were saying (he's been zapped by Pikachu enough times that it could have let him pick up the language)