You have it backwards. They can’t fire you for an illegal reason. These are known as protected classes. But they can fire you for any reason that’s not protected. And “no reason” isn’t protected, so it’s legal.

For the curious, the protected classes are: Race, color, religion or creed, national origin or ancestry, sex (including gender identity, pregnancy, and sexual orientation), age, or disability.

So you can’t fire someone for being black, but you can fire them because you don’t like the way they smell, because you don’t like their personality, because their favorite color is purple, or just because you feel like it. As long as you don’t say you’re firing them for one of those illegal reasons, it’ll be very hard for them to sue.

And employers know this, so they almost always list it as “no reason” to avoid any potential lawsuits from words getting twisted against them. For instance, maybe you fire someone because you don’t like the way they smell, but then they try and twist that into “you fired me because I smell like curry, and therefore you fired me for my race.” So to avoid anything potentially being used against them, they’ll simply list it as “no cause.” Unless the firing was for cause, (which basically means you fucked up while working there,) and they want to avoid paying your unemployment insurance. In those cases, they’ll build a case against you, then fire you once they have a binder full of real/imagined company policy violations to throw at you.

The only way OP would be able to sue is if they’re able to prove a pattern of behavior against a protected class from the employer. For instance, maybe a new manager gets hired, then every single black person gets fired within the next few weeks. If those workers come together, they can show a pattern of behavior that the manager is racist and fired them for being black, even though the manager didn’t explicitly state that the firing was due to racism. But that’s hard to prove and requires a lot of documentation on the employees’ part.