It doesn’t feel good to feel excluded. Being told that you’re not wanted in a space/event/group makes people have an immediate reaction. I will certainly let people have their spaces, I’m just offering why I think it happens. Like you saying about the friend that wasn’t invited. The friend being upset wasn’t upset because he wanted involved in that game. They were upset because they weren’t invited. That can make you feel unimportant, overlooked, or forgotten about. In terms of friendship, it’s better to make the offer and let the person make their own decision. Unless of course you have invited the person in the past and they like blew up at you for even asking about something you know they hate. In that case I’d say not inviting is best.