Funny, you can use propositional logic symbol, but you don't understand what they actually mean.
In either case, your argument seems to simply boil down to what you perceive as "damage". So basically, you are quantifying it(let's say a function D that evaluates it) and then stating that(suppose that F is the set of 'female' and M is the set of 'male') that for any f E F and m E M, D(f) > D(m).
In other words, that the 'damage' received by any woman will be greater than the 'damage' received by any man.
We needed to organize your argument in the first place(as it's a mess), in order to disprove, as there is simply no way to disprove a spaghetti.
It's sufficient to show a single counter-example. As yourself have define, some rapes are realized through violence, in which case we can just show that there are damages done through violence which are greater. Such as supposed that as part of the rape, a woman(or a man) hits a man(or a woman) in the head with a brick, this causes a concussion and several neurological damage. The victim then suffer from the rest of their life. This is greater than the other risks you have outlined.
So basically, it would boil down to "how can you be so sure that your quantification of damage is actually true?", of which I am willing to bet that you can't. You have picked a couple of things, decided they are enough and run with it.
Want other examples of factors you haven't considered? Social stigmatization, child support, physiological damage, etc etc
