Donít blame yourself for the letter. First off, in a healthy relationship you can and should be able to express vulnerability without it being turned on you. So you did nothing wrong. And trust me, if you did not give him the letter, he would concoct other reasons. Are you familiar with gaslighting?
Reading your post, I see tremendous emotional abuse. He acts angry towards you. You try to ask why he hates you and then he says that is why he canít talk to you. Classic gaslighting. He creates situations to make you to blame because he needs an excuse for how he feels.
You had a partner who could not care for you or your child when you both needed it. Strong men want to care for loved ones. That cold dynamic you saw from his family during that show should look very familiar to you in your husband. They are emotionally constipated.
Stop blaming yourself. Heal. Strengthen yourself. Raise a good man. You are the prize.
Me 41, H 47, M 15 yrs, S11, S13 BD 1: 11/4/14 we work on it; really I pretzel myself BD 2: 3/31/15 H goes down to "dorm room" 8/15: H back to MBR 10/15: H back in dorm room 1/18: H files, now divorced