It's a little harsh, and that's the message interrupting conveys. If that's not what you mean, breathe, have a little patience, see if you can figure out their eye colour and listen to what they're saying.
Interrupting erodes conversational rapport and makes people feel like they're not being listened to: They're not. Right before you interrupt you were figuring out what you were going to say instead of listening.
Let conversations breathe a little. Leave gaps between when they stop talking and when you start. It lets you sound reflective.
Avoiding interrupting also allows you to listen more fully to the person doing the talking. Perhaps more importantly, it lets them feel like you're listening.
Asynchronous communications, like texting, let both sides finish their thoughts, even while the other person is typing. That doesn't work so well face to face.
You can get away with occasional interruptions if you know the person you're talking with is direct and cuts other people off regularly. They are less likely to take offence if you cut them off.
Practice catch and release conversations. Here's how:
Catch: When it's time for you to start talking, refer to something they just said.
Talk: This is where you say what you want to say.
Release: Ask them a question so they know it's their turn to talk.
Listen: Making 'listening sounds' like uh-huh isn't interrupting. It's encouraged and conveys that you're paying attention.