There are 14 verses in the passage addressing head coverings for women. Your whole argument rests on a single verse. Try to make you case without that one verse.
It's very common for people to see their non-biblical doctrines in the Bible. A psychologist calls it bias confirmation. I call it people just trying to rationalize their rebellious behavior and doctrines. And, there's no shortage of false teachers to tell people they're right.
Paul says, "A man who prays or prophesies with his head covered dishonors his head, but every woman who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven. For if a woman will not cover her head, then she should cut her hair short. But since it is disgraceful for a woman to cut off her hair or shave her head, let her cover her head. "
Without calling long hair a covering in the above quote, Paul links long hair to a head covering, but necessarily not as the same thing. If a woman doesn't cover [that's a verb, not a noun as you seem to think] her head, she might as well shave her head. Therefor, long hair can't be the head covering Paul says women should wear. It's simple logic, if you're willing to follow it. As it is, you're just dismissing most of what Paul says as a convoluted way to say women should have long hair.
If you want to continue your position, could you explain why Paul uses a totally different word when he says a woman's hair is a covering vs. when he says a woman should have her head covered?
The single verse that you extract out of context is just an argument (Paul's third argument to wear a head covering) that women should wear head coverings because long hair is a covering showing women should wear a covering (over the long hair).