Hmm. This happens a lot with my sister and I haha. She just has a terrible habit of cutting me off when I'm saying stuff and used to be it really made me annoyed but eventually I got over the fact that it's just one of her more idiotic traits that she needs to get rid of eventually. But for now, to prove a point I raise my hand whenever I get cut off and stare them down until they let me talk again. Someone else said they turned it into an entertaining game because it wasn't worth the effort of getting mad and now she counts how many sentences she can fit in until someone cuts her off.

I guess the main thing is, while you have the right to be irritated, I would advise you try your best to not let it get to you as much because there are a lot of people who do that. Whether in school, in work, in meetings, and etc :P there are rude people everywhere but don't let them ruin your parade. They can only annoy you if you let them!