Gorillas and chimps can be taught to communicate using deaf signing conventions but they cannot be taught to speak English, and that's because they do not have voluntary control over breathing likie we do. Koko, the first gorilla taught to sign, is said to have an understood vocabulary of thousands of English words and understands English speech, but she cannot speak it. The same could easily have been true of neanderthals.
Modern humans have voluntary control over breathing since we apparently originated in water, and control over breathing is a necessary adaptation for swimming.