Men are sloppy pigs.
Women are petite fleurs.
Men only need to leave the toilet seat down when, umm, you know (not #1).
Women, on the other hand, always need the seat down to do their business.
Men are inherently lazy.
It takes just as much effort for a man to lower the seat after he is finished as it does for a woman to raise the seat after she is finished.
A man will not bother to lift the seat up if it is already down, and will thereby leave splashes on the seat. Because, you know, men are sloppy. This creates an unpleasant sensation on the delicate rump of the female as she sits down, never suspecting that someone (a man) would be so careless with his wee wee (aka "tinkle" for the women).
Conclusion: it is far better for a woman to lower the seat when she, umm, you know, than it is to rely on nasty men to be considerate and lower the seat after they are done - or, more importantly, raise the seat before, umm, you know.