However, there is a clear distinction between how the law defines rape and the motivation of the rapist in committing the act. You are arguing the former aspect of rape and others are arguing the latter; both are valid.
I think what others are pointing out is the rapist seeks above all to dominate and humiliate the victim, and uses sex as a means to increase the humiliation of the victim far in excess of what simple assault inflicts. But sex is not the primary motivator for rapists, otherwise they would simply engage in a consensual arrangement involving rape fantasy.