U.S. Supreme Court in Spectrum Sports, Inc. v. McQuillan 506 U.S. 447 (1993),
"The purpose of the [Sherman] Act is not to protect businesses from the working of the market; it is to protect the public from the failure of the market. The law directs itself not against conduct which is competitive, even severely so, but against conduct which unfairly tends to destroy competition itself. This focus of U.S. competition law, on protection of competition rather than competitors, is not necessarily the only possible focus or purpose of competition law. For example, it has also been said that competition law in the European Union (EU) tends to protect the competitors in the marketplace, even at the expense of market efficiencies and consumers."
In this case, BofA could (but probably won't) claim that McMillan is attempting to unfairly deny their customers the same use of their credit cards that McMillan grants to the customers of all of BofA's competitors - creating an unfair competition for credit.
Let's make this clear - I think the BofA decision is a bad one. However, I defend their right to make decisions based on information available to them, and with the consent of their shareholders. Kinda like free speech - I may think what you say is (fill in the blank), but I defend your right to say it.