Re: Banned from Aikido...
So you want to "fight" someone because they think they are a better fighter than you. Do you challenge everyone who thinks they may be more skilled at something than you? If you do I'm afraid you're going to be busy for a while because there is always someone out there who will think they are better than you at some activity (martial arts, swimming, running, basket weaving, etc.).
You also mentioned fighting without hurting each other which mean some rules come into play. If there are rules you are really not fighting. All you are doing at that point is seeing who is better performing under those rules.
I don't know you or your instructor but based on this discussion in my opinion if you can't let go of your ego it sounds like the dojo you were at may not be a good fit for you.