I'm going to push my friends away after they hung out without me and didn't make an attempt to reach out to me when I didn't show up
Why would you push them away?
I feel left out... they don't appreciate my friendship anymore.
I understand you are upset they did not invite you. Do not push them away, but instead tell them that you felt left out, they will understand.
Fine, I'll suck it up.
It is good you recognized that you need to talk to them. Pushing away all of your friends would make you feel worse than just not being invited out once.