Vegeetas,
for what you have been through. I have known several men who are rape victims (in their case the perpetrators were other men) and on a moral level, I can see why you would want to count what was done to you as rape rather than sexual assault.
However, here we are using the legal definition of rape in order to get a handle on the way official statistics are being distorted and in fact rendered meaningless by gender self ID. Rape is one of the few offences which because of its legal definition means that it is very hard to cover up the fact that the vast majority of the perpetrators (barring, as pointed out, a tiny minority of women prosecuted under common purpose) are unequivocally, unquestionably biologically male.
As for the "have to be mentally ill to rape", sadly not. The work of American criminologist David Lisak is very interesting in this respect. He uses questionnaires with questions like "have you ever had sex with a woman who has said no, and you've gone ahead by physically restraining her?" (i.e. questions describing situations which meet the legal definition of rape, but don't use the actual word "rape"). He finds about 6% of American male college students (his chosen study group) will admit to actions meeting the legal definition of rape. (When he repeats the questionnaires with the word "rape" overtly in the questions, 5% will admit to being rapists).
Sadly it's not a tiny minority of mentally ill men, and it certainly isn't monsters - this is a sizeable minority (1 in twenty - two or three or four in every busy railway carriage you've ever been in). And they look normal. For the most part they act normal. They probably help old ladies across the road sometimes. They may have offered to get milk for a housebound neighbour during last week's snow. They're probably respected in their workplaces. They vote Tory... and Labour and LibDem and Green. They wouldn't dream of kicking a puppy. They may well run half marathons for cancer research. They maybe give up Saturday mornings to help at their sons' sports clubs. But they still rape.