The case that baker Jack Phillips brought before the supreme court was largely one premised on his cakes being forms of expression that were protected by the First Amendment. It wasn't the only reason his case won - the decision in his favour seemed to turn on the fact that the Justices considered the baker's religious sensibilities to have been disrespected in the lower courts. This argument however focusses on reconstructing the case that Jack Phillips' lawyers brought to the Court.
Both baking a cake and creating flower arrangements is a form of artistic expression - the Colorado baker was adamant about how personal and individual his work is. In his words, every cake that leaves his shop contains a personal piece of himself. What's more however, he argued that by crafting a cake for a same-sex wedding, he would be making a speech act in favour of same-sex unions - something that in actuality he is deeply opposed to. By forcing the baker to create this cake, you would be violating his right to freely speak against same-sex weddings. To understand this argument it helps to imagine a different scenario. For example, we think that it would be understandable for a gay baker to refuse to bake a cake depicting strong anti-gay imagery; or for a black baker to refuse to decorate cupcakes celebrating apartheid. Forcing these alternative bakers into accepting these jobs is a violation of their right to control the ideas they endorse and speak for. This was the pivotal piece of reasoning that swung the supreme court in favour of the baker. Forcing an individual to speak in favour, or against, an institution/idea/principle is violence against that individual and incontrovertibly violates their first amendment. As the first amendment is the source of many other rights, and is the basis for a healthy democracy, it's prioritisation is reasonable and important.
Certain services that business provide are speech acts Forcing a business to support or condemn something against their will is a violation of their free speech Free speech is more important than individuals' rights to services We mustn't compromise businesses' right to free speech for the sake of access to services