It can seem like an overly intellectualizing exercise to differentiate between many different styles of bellydance, and there are a lot of contentious discussions about what makes a style of dance and when something ceases to be bellydance anymore. While it is understandable why one would want to avoid that kind of conversation there are many reasons for learning about the different styles of bellydance. Selfish reasons, practical reasons, and socially conscientious reasons.
First, let's differentiate between bellydance and Middle Eastern dance. Many styles of bellydance, but not all, are Middle Eastern dance, and a fair few styles of Middle Eastern dance are bellydance, but far from the majority. Nadira has a wonderful diagram that makes more sense of in a smaller space than my rambling about it will. It's also worth noting that in order to talk about one style or another, you HAVE to talk about the time period you're referring to. Differentiating between Turkish and Egyptian style, at least as enjoyed by the upper classes, would be useless if you're looking during the Ottoman empire when fashionable entertainment was Turkish. But during the 1960's, for example, the two countries had very different styles.
Also, remember that there is no value judgement in differentiating styles. I advocate doing it so we can appreciate each style's unique contributions and beauty, not in order to berate anyone into a mold.
It's a good idea to learn to do more than one style, but there's a lot of them! At the very least we should all learn about all the different manifestations of bellydance. Now, down to the reasons why it's worth it!