There's no way osu! is going to slow the computer down. Your dad's simply extremely ignorant about computers. Irresponsible downloading WILL slow down the computer, because you'll end up borking the registry, catching spyware/viruses, etc.
osu! is in no way an irresponsible download. It's reasonably small, independently developed by one guy in his free time, contains no spyware, adware, or viruses, and has a pretty big community following it, which probably wouldn't be around if this program was damaging in any way! Explain this to your dad, and maybe he'll let you download it.
Oh, and your dad saying he'll know if you downloaded it? That's bullshit. He may know if you download something irresponsibly, but this? Impossible unless he's tracking the internet traffic. And as ignorant as your dad seems to be, I think we can rule that out.