My older brother is a really fast talker.
Why did you say that you love me the most so quickly?
I’ve never seen such a fast talking baby before.
When you have a fast mouth, you're probably a fast talker, right motormouth?
Remember how body parts often change even jukugo words to kun'yomi readings? That's what happened here too. Both readings are kun'yomi, making this one はやくち. Alternatively, you can read this as はやぐち as well.