A different perspective here, a slight twist if you will.

I find it interesting how often you are willing to sacrifice your relationships with other people because they won't change for you, even though you have told them it will end their relationship with you if they don't.

They are the passive agents here. They do not choose to leave you. They are just being them. You are doing the leaving.

From an external perspective (going only by what you have written here of course) it seems:

You want something from someone or you want them to change in some way
They don't want to give it (or change it)
You say "If you don't give me this thing (or change this thing) I will leave you."
They likely really don't want you to leave but stay true to their own needs/beliefs etc
You leave.
They are shocked and sad. They really didn't want you to go.
You are sad. You didn't really want to go.

They are being them.
You are being you.
You are doing the leaving.

I wonder what it is that is so painful, so hurtful, so overwhelming for you about someone not being willing to compromise themselves that you feel compelled to flee the relationship altogether? It must be very, very intense for you, because it seems stronger than allllll of the good things that those relationships offer as well.

What is the thing that makes a person not being willing to compromise on certain points so incredibly hard for you? It isn't about the hug, even though it is the hug that has triggered this overwhelming need to flee this time. The overwhelming need to flee existed before the hug because you have had to flee when this same thing has been triggered before.

I wonder, when was the very first time you felt this way?? Worth looking at.