You can choose other reasons or just not give a reason.

Are you even reading?

It is legal to fire someone for any reason or not reason at all. However, that doesn't stop the former employee from lying and saying that you fired them because they were black.

To win a civil rights act case, you don't need a quote of them explicitly saying you were fired because you were black. You can prove to the court with more circumstantial evidence.

If you were the only black person in the department and you can prove you were performing equally well as your other coworkers, for example. If you can then cite a racist joke your superior made that you overheard, you have an even stronger case.

You may have actually been fired because you weren't performing well enough, but if you can conjure numbers that show you were, even though they don't paint the whole picture, you can make a compelling case it was because you were black.

This is literally why HR departments are so prevalent, even in at-will states. They're there to protect the company.

I understand the law. You also seem to understand the law (although you clearly forgot about the Civil Rights Act until I reminded you). But you're not understanding people or courts or how they all act.