People just out of enthusiasm or fear cut other people off in the middle of their sentences.  First of all, because they've got something they think must be said then----and also out of fear that the talking will roll along and what they want/need to say will be lost.

Unfortunately, that's very rude and disrespectful: fueling anger, resentment, and fighting.

But if people know they will have THEIR OWN SPACE to speak, then they'll (however impatiently) wait their turn.

So make it clear that each person has a space to speak, uninterrupted---assuming they give that courtesy to others.

Dan