For most of my life I've never been a very patient person.
I interrupt people when they're talking, I finish nearly every sentence someone has to say, and if I don't feel like listening to someone or contributing to the conversion, I will completely disregard them, or talk to them coldly and bluntly. Overall I come across as pretty rude. These behaviors are especially bad if someone is speaking to me about something sad, troublesome, etc., which immediately makes the situation worse when I behave the way I do.

Don't get me wrong, I genuinely feel bad after doing these behaviors, but I get so lost in the moment of being impatient/agitated that I don't realize/care what I'm doing until after I've done it, and by then the person who is trying to talk to me probably feels pretty unimportant.
I don't want to be a jerk anymore. How do I become more patient and less agitated when speaking with people?
Thank you in advance!