Can I abruptly ignore someone I've known for years?
Why would you abruptly ignore someone you have known for years?
I don't understand why they want to befriend me
You are being rude to your friend by ignoring them. If you don't want to be friends with a person anymore than you should confront the situation and be more honest than you are being.
To be clear I'm not being rude, I just don't understand why they want to befriend me.
You seem like you're feeling a bit hard and down on yourself with not being able to understand why people would want to be your friend-- but don't let that out on someone who is trying to care about you! Losing friends hurts and if you have no one to turn to then you'll feel extremely regretful that you let those who cared go away.