Speaking for myself here:
Don‘t try to prove anything, other than that you are the world‘s best infanteer. Don‘t use your sex, and don‘t hide behind it. There are plenty of men out there who do stupid things to "prove they‘re a man". Don‘t fall into a similar trap yourself.
Listen to your instructors, run your heart out and remember a few things:
1) Women are usually less physically strong than men. They can train up, but testosterone builds muscle mass a lot quicker, and a strong man will almost always be stronger than a strong woman. It‘s not personal, it‘s biology. Taken as a general point, don‘t let your mind write cheques your body can‘t cash. A zero balance in the account occasionally won‘t kill you, but the overdraft charges are a bitch. ;-)
2) Women have the physical and mental capacity to be better at endurance than men. They have to be. In the grand scheme of things, it is women who keep the human race going. ;-) Be tough. Don‘t let anyone make you a quitter.
3) Men tend to think differently than women. Use you own thinking to your advantage, it may screw up the opposing forces. But don‘t reject other ideas or common sense because of it. When you become a platoon leader or officer you‘ll need to see both sides of the coin anyway.
4) Social rules are different for men and women in society, and this point is accentuated by the primarily male environment of the armed forces. Think of relationships as relationships in the office, or relationships in the same class. Very difficult to keep secret, and they *must not* interfere (or even be perceived to interfere) with your work in any way. As you know, there is a double standard for women. Sad, wrong, etc., etc., but still true. You need to be above reproach, particularly if you become an officer.
5) Be a responsible individual. If you are running the rain and you forget your raincoat, don‘t take the one offered by the guy next to you unless it‘s an extra. No special treatment asked for or accepted. You‘re just another troop, *gurl* or not...Make sure that you know this, as well as any well-meaning troopers who may attempt to treat you differently because of your sex.
I‘m a Canadian taxpayer, I expect you to keep me soft, fat and happy, with my 2.3 kids and my house in the ‘burbs.