Well candidus_cogitens that is a tough question... I’ve only been on this position twice in a long time gaming (15 years), and I must admit to not being proud of how I handled both of them.
One time the players was disruptive, loud, obnoxious and was creating friction and tension in the group and we all decided he had to go. We told him we were going to take a break form gaming and we’d call him when we got back together. WE started playing again in two weeks, but never called him.
This guy was an acquaintance, and while I felt a little guilty, this was not somebody I cherished as a friend.
The second time was different. This person I had known a long time and we had been close on and off, and I sincerely appreciate him and think very highly of him. Still his gaming style was confrontational, very combat oriented in my more role-play oriented campaign, and his outburst had gotten the better of me.
I think I am a fair DM and had done my best to accommodate him and his ideas to the ongoing campaign. When he opted to bow out of my AD&D 2nd Ed campaign I was finishing, until I switched to 3rd Ed he wanted to play, I accepted his decision, but never called him back when we did start playing 3rd Ed.
I still feel bad because I miss this guy, but he could not separate the game from the real life friendship I thought we had. That makes me very sad still, and it has been over two years.
My recommendation… Be forthcoming, clear, and firm. If this is something you are not willing to negotiate about, simply speak your mind calmly and politely. I think sincerity is always the best policy, even if I did not do it… I hope you can learn from my mistakes!
Best of luck…