I'm on the supply side of the labor supply-and-demand curve. I set the price that I'm willing to sell my time at. Nobody else sets my price, and I don't set anybody else's price. On the demand side, there are a bunch of employers who each have their own price for what they're willing to pay for a certain set of skills. Each sets their own price. Nobody else sets it for them. In particular, nobody on the supply side can possibly set the price the demand side is willing to pay.

Now, all of what I just said presumes a functioning supply-and-demand market. It breaks down if there's collusion between employers, or in a single-employer situation. Unions may well be needed in such situations. But in a working labor market, demanding more than market price for labor will result in lower demand for labor.