Cutting people off mid-sentence announces that your next thought outranks their current one. People keep track.

Interrupting delivers a message about rank whether or not you intend one. Your thought arriving on top of theirs says that yours could not wait, and people notice this more reliably than almost anything else you do in conversation. Enthusiasm is a real reason for it and does not change what gets registered.

Try letting a full second pass after someone stops talking before you begin. If you are worried about losing your point, write three words down and let them finish.