I need help forming an argument against Indiana's new law?

I got into a debate about why the bill should be struck down and when I actually got into the argument, I knew what people were saying was wrong but I couldn't formulate exactly why. So I need help kind of making a sound argument.

Main argument for the law: It's a business owners right to do business with whom they choose. If its against their religion to serve customers they shouldn't be forced to. Gay people should just go somewhere else to do business. Business owner's have the right to refuse service.

Main analogy for the law: It's like a business owner who makes stickers refusing to serve someone who asks them to draw a the prophet mohammed, the business owner shouldn't be forced to do it.

My argument against the law: The law is the same thing as segregation. You can't do business here but you can do it else where? That's familiar with you can't go to school here but you can go somewhere else. Furthermore, serving gay people isn't a sin in any religion, it's typically sodomy. That would be the same as refusing service to overweight people because gluttony is a sin, or refusing to serve veterans because you're a pacifist. This law also significantly impacts the life of gay people because Indiana is so rural that if you were refused service in a small town with 1 pharmacy, then you would have to drive to another town and hope that they will serve you.

Main argument against the analogy: That's not discrimination based on the the definition of discrimination.