This is accurate in as much as you do have different functions in your left and your right brain.
For most people, speech perception, language, listening to other people taking and producing your own speech is something that happens on the left side of the brain. And for most people, stuff like understanding music, understanding emotion in speech, or recognising who is speaking and things like this are on the right side of the brain. You can find a greater involvement of the right side of the brain with maintaining attention, in processing faces, too: a lot of things that you might thing of as processing social information, other than the actual content of language.
"The split of functions between the two sides of the brain is true for everybody"
What there isn't is any evidence for whatsoever is that this is systematically different between people. This split of functions between the two sides is true for everybody: you don't find a “left-brained person” and a “right-brained person”, which is often how the terminology ends up getting used. “I'm a left-brained learner”, sort of thing. That's just not how it works; people are all using both sides of the brain all the time. People use the short hand of “logical” versus “emotional”, and maybe very crudely you could split the two sides of the brain's activity like that — but that doesn't mean that if you tend to think more logically that you use your left brain more, or that if you are more emotional you use the right more.