I have the right to freedom of speech. You have the right to freedom of speech(assuming that you're an American citizen).
If you and I form a partnership with the express purpose of working together to combine our voices and speak together, we retain that right to freedom of speech.
That was what Citizens United held.
Beyond that, you're just plain wrong. Corporations are legal persons. Only persons can be parties to legal actions. If your neighbor's dog escapes and bites you, can you sue the dog? Of course not. You sue the neighbor, the person responsible. If your neighbor kills your dog, can your dog's puppies sue your neighbor? Of course not. Again, non-persons cannot be party to legal actions. A corporation can own property, pay taxes, sue, be sued and as a legal person, corporations have rights. They don't have all of the same rights as people, that's why I find it so frustrating when people conflate "people" with "persons". Legally, they are different concepts.