Being 'third wheeled' isn't a nice feeling, I've had it happen to me enough times to know, so why do people do it? I would never make plans with a person, randomly bring a friend along and then just ignore the person who was kind enough to invite me along in the first place. I just don't understand how some people think it's socially acceptable.
I think that this hatred of being 'third wheeled' is the reason for my love for even group numbers. In my head if there is a group with an odd number of people in it someone is inevitably going to get left out (most of the time it's me), but if you have an even group everyone has a buddy and someone isn't going to end the day feeling alone and disappointed. I'm sorry if you think differently. But this is how I feel. Rant over!