It is also possible that monkeys do not take turns when speaking because this turn-taking is a learned behavior. This particular finding is hard to prove, however, because the two studies that looked into it had opposing conclusions, and rather different methods. Nonetheless, it's an interesting concept to take into consideration.
Another bit that I found quite cool was how humans and songbirds both have a set of genes involved in rapid articulation and sound sequencing that other species do not. The author, Charles T. Snowden, predicts that this could be the reason for monkeys not exhibiting similarly complex speech. But in reality, we don't know why other primates don't talk as we do. Yay for the unknown!
A link to the article, if you're curious: http://science.sciencemag.org/content/355/6330/1120.full
P.S. Sorry to post so much so late... I thought we were only supposed to post 2 times. Completely my fault.