I think your self-interest in this case could be justified under all three approaches, except maybe the deontic.
From an "invisible hand" perspective you cannot possibly know that you are "equally good" in advance and this is precisely what the rules are meant to determine. Presumably the meritocratic outcome serves to increase overall utility of the team or economy or whatever, or at least that is the theory. You and your antagonist are parts of a larger utility system, not two different and "equal" utility systems.
From a virtue standpoint, you have a duty to pursue excellence, in this limited case according to the rules of team construction. Of course, you could be pursuing a higher excellence, such as Christian charity, Stoic self-control, or the ethos of chivalry, with which the Church attempted to dissuade jocks--I mean knights-- from brutish, wasteful jousting. (Of course, "virtue" derives from "virility," so culturally that's a heavy lift.)
The trickiest case is deontic. Here it seems that deference to your opponent might be positively bad. We assume you both want to be on the team because it is somehow meaningful. Yet if we universalized your "will to withdraw" you would subvert that value entirely and, defeating your own "noble" purpose, hand your opponent a now "meaningless" spot on the bench!
I'm not sure if Kant sorts through any similar cases, but to me at least this looks pretty clear cut, and a kind of oddity. The presumed good in this restricted world can only be derived from competition and thus self-assertion. Were everyone put on the team, or were everyone to withdraw, then whatever good inheres in "teamness" becomes incoherent.
As a backup demonstration, let's just think of Kant's CI as a formalized golden rule. Would you want to be on the team by virtue of the fact that your competitor withdrew so you could have your way? Only a truly narcissistic, lying, authoritarian former casino-owner could truly want such an outcome...