It's out of courtesy that you should put the seat down or put the seat up. You can throw love in there... but I sure as hell won't prioritize it as something that I would base my relationship on.
The seat doesn't stay down while guys go to use it because although we can aim DURING the flow of urine, it goes in random directions at the very beginning and at the very end, ending up on the seat itself. To give you a mental image, try pinching a garden hose before turning it on, then let the water pressure straighten the flow out. Where does the water go at first? Where does it go when you go to turn the water off and pinch the hose? Nobody knows.

And I'm sure that I don't even need to get into the random postures that a guy has to attain to urinate with "morning wood."
It's not a straight shot every time, girls. That's why urinals are designed the way they are.
As far as remembering to put the seat down "out of necessity," I can't remember the last time that any girl put the seat up for me.
I don't know about you, but I wash my hands after I use the bathroom, so that removes the whole nastiness/germ argument.

If anyone is really that squeamish, use a couple of sheets of toilet paper, or apply pressure to the side of the seat to bring it up instead of actually grabbing it.
P.S. This is a great discussion.