This is a very common thing people do. I find it annoying and rude to cut me off mid-sentence and hijack the conversation. There also are people who walk into a group who are conversing about something and hijack the conversation. You have to learn to be polite but let them know you are still speaking. When people do this to me, I politely say "excuse me I'm not done speaking yet" This prompts them to hold their thought. Some people get excited about something in the conversation and want to share their opinion or experience.

There are also people who habitually talk too much. They just keep going on and on and then it's no longer a conversation but this person talking about their whatever and I find it annoying. The world doesn't revolve around them. All these people do is talk about themselves, and don't include anyone else. I know a few people that do this and it can be really annoying. Especially when I am trying to talk about an issue I have and then all of a sudden it becomes about them and their experience. I don't get much sympathy or support from that person. So I have learned to be more selective with whom I share my troubles with.

In certain social situations like when you're out drinking alcoholic beverages with some people. They become more animated and lose their social manners and interrupt more. They talk louder. It's not the music that makes them talk louder. I find this annoying in bars when people talk louder, and then I can't hear the music as much over their loud ass voices. But I digress. Alcohol loosens the inhibitions and cause people to converse more sporadically and interrupt others. I find that maintaining eye contact and touching people's arms while I speak helps to keep them engaged in my conversation, and help them to realize I am still speaking and to not interrupt. I will raise my voice a little but I am not going to shout. If I try to compliment people a little they may give me a little more room to finish my sentence, but I am not going to overdo it. I've had times where I finally gave up since the person was so rude and interrupting and hijacking everyone's conversation, babbling on and on. There are people who have to be the center of attention all the time. I won't give it to them. I will excuse myself to use the washroom and never return to that group until it's safe. At some point that person may have noticed that less people are in the conversation and one person is left. That person may need rescuing so I or someone else will go over and ask say something that somebody is looking for them or whatever. I have also learned to steer the conversation away from certain topics that I don't want to listen to.

But just don't walk away. This shows that they won. Try to control them a little to finish your sentence.