Who is always offended and upset by any perceived slight to them?
This is going to be a bit of a rant...
Some examples
Leaving a mutual friends house I bump into them at the gate and they say "Is it something I've done?" Errr no, I wasn't thinking about you when I decided to leave the house 
Passive aggressive posts on social media when you meet up with mutual friends.
Having a gathering for your birthday, them finding out about it and asking why they weren't invited. This one pissed me off no end cos I can choose who I invite to my own home.
They're not going to be a friend much longer if this carries on. I'm tempted to block them on my phone but I feel really guilty doing so and I think they'll send their flying monkeys to find out why.
How would you handle it?