The ATC union is a monopoly, which is just as bad as a business that has a monopoly. They can hold the entire aviation system in the US hostage. This is why it is illegal for them to strike.

They knew when they took the job that striking was illegal. Reagan reminded them of that, and said he'd fire them if they broke the law. They did anyway, and Reagan wasn't bluffing. Reagan could have also prosecuted them, but (wisely) chose not to.

Firemen and police officers are also usually not allowed to strike. For the sake of continuation of society.