The reason is not to do with words or 'it's short for', it's because, when the garment was developed, they thought it looked like a capital T. No neck, short arms, straight-body. It's a T. Ergo, T-shirt. Not t-shirt, not tee-shirt and certainly not t-Shirt. It can be shortened to tee, or T, as in "hey dude, grab my tees from the dryer," or "That colour T doesn't suit you," but that's about it.
Weird the things that bring on a rant.