What's the big deal with leaving the toilet seat up?
The way I see it, men approach the toilet face forward. Therefore, if the seat is down, they can see that right away and lift it. No harm, no foul.
Women approach the toilet facing the other way. If the seat is up, they might not (probably won't) notice, especially if they are going in the middle of the night. Not noticing the seat is up means an unpleasant surprise when you end up sitting on the rim (yuck) or worse, falling in! (double yuck)
That's my take on it, anyway.