It’s normal to feel guilty. I am familiar with the feeling especially if the person is reacting in this manner like crying etc Remaining unaffected was a reaction you needed in order to get through. It’s normal too. If you start bawling too who knows how it would end up. Maybe you’d not have guts to go ahead with divorce
I think maybe to help with that think that you weren’t leaving/asking to leave an innocent child, elderly family member, incapacitated person. You weren’t throwing them out with no means to provide for themselves in the middle of sub zero temperatures in the blizzard.
You were ending it with a grown man and I am sure he was leaving having place to go to. He has family and friends and he wasn’t going to sleep on the streets. Him crying well people often cry at break ups.
And shortly after he went on telling bad things about you to his friends. So much for snots running out of his nose Purge it out of your mind.