So, you're wrong. But you probably already knew that.
In the case of the baker/cake/gay-wedding:
When you operate a business of public accommodation, that is, a business that is open to the public, you have to operate under certain rules and laws. One of those laws is that you cannot deny service to a person solely based on that person's inclusion in a protected class.
Now, federally, there are several protected classes. They include, sex, age, nation of origin, and race. (This list is not exhaustive.)
Now, that means, if you operate a business open to the public, you cannot refuse service to someone simply and solely because they are a woman, or because they are black.
States can add to the list of federally protected classes, but may not remove anything from that list.
Colorado, where the bakery/gay-wedding case took place has added sexual orientation to that list.
Which means that the bakery could not, legally, refuse service to the couple simply because they are gay.
If the bakery had been booked solid, and could not have produced the wedding cake in the time required, it wouldn't have been a discrimination case.
If the bakery didn't even offer wedding cakes as one of the services they offered, it wouldn't have been a discrimination case.
But because they do make wedding cakes, and because the owner made it clear he wasn't selling the couple a wedding cake because they were gay, it was discrimination, and it was illegal under Colorado's laws.