There are actually a number of answers to this question, but one of them is quite simple: because there are so many others nearby who are happy to do so.
One amicus brief filed in support of Jack Phillips by numerous law and economics scholars, including the esteemed Richard Epstein, makes this point quite nicely.
That brief points out that according to a search on Gayweddings.com, there are 67 other bakeries in the Denver area alone that are willing to create a same-sex wedding cake, including one that is only 1/10 of a mile from Jack Phillips’ Masterpiece Cakeshop. Forty-two of these bakeries are shown below; notice where they are compared to Jack’s shop, marked by the orange circle:
Given all these shops that are happy to create a wedding cake for a prospective same-sex couple, is it really necessary to force Jack Phillips to be the one to do so?
While the prospective customers may be offended at Jack’s beliefs, part of living in a free country is that we interact with people who believe differently than us.
Yet they can easily travel nearby and obtain the cake from someone else—someone happy to help create it.
Meanwhile, forcing Jack Phillips to create the cake comes with the heavy cost of forcing him to violate his conscience or stop designing wedding cakes (and potentially go out of business).
Regardless of our personal views on the issue, that is not a vision of American “freedom” that any of us should want to be a part of.