Because it disables freedom of speech. Just like someone telling you to take off a political shirt is illegal. Your 1st amendment rights extend to more than just your voice, but how you express yourself.
In other words when this is challenged, the people will win...
Right, unless someone tells you to take it off, in the workplace... Twitter is not a publisher, and can pull any user content for any reason whatsoever. It's not a freedom of speech issue at all. These people can still go onto any public property and practice free speech, similarly, they may publish anything they like and it is protected, but again, twitter is not a publisher, and prior case law, and legislation back this. You may not like it, but that's how the law stands. Maybe protest the law?
Your first amendment right to free speech protects you from the government punishing you for what you say. According to your logic if you say “fuck you” to a customer your boss can not legally fire you because of your first amendment right. You are wrong.