It isn't necessarily intentional.

A lot of dudes have no idea how to actually aim their junk. Other times, you might get an unexpected spray. They might be in a hurry and just not aim beyond facing the toilet. And you've got splashes from usually forceful urination. There's probably people that do it intentionally.

The real question is why the fuck they don't clean up after themselves.

It’s not always pee. One of the public restrooms I’ve had the displeasure of using repeatedly (it’s on campus in a building I frequent) has toilets and urinals with extremely high pressure flush action. Every time you flush the pressure is so violent that they spray water all over the place, including on the seat and all over the floor. They’ve been like that for years and never fixed.

What’s especially rich is that there’s sign above the urinals which says “your aim is appreciated” which makes me laugh every time. I’m so careful using the urinal not to spill even a single drop on the floor, then I flush the damn thing and it makes a huge mess!

Probably because the last guy pissed all over the seat, and they didn't want to sit in piss

I always wondered why too; maybe they think it’s “gay”? Or possibly playing Fireman Sam or something?

Probably also kids. The urinals tend to be to tall for them to use and they don't have great aim.

Or at the very least lift the seat.

Guessing they also don't close the lid so they get to spray themselves with whatever's in the bowl when they flush. And then don't wash their hands before leaving.

I've seen evidence of people doing long range pee with the seat down in the UK when I went to visit.

Or just, you know, sit to pee like a civilized person.

Urine is sterile. And by washing the seat with piss, you’re performing an antibacterial favor for the next guy.