I know it always supports big business. And it’s a reactionary force that people in power turn to when things go badly for the workers and they think of revolt.
But fascism also demands genocide and killing of millions of people and that would only hurt the capitalists, no? Because these are people who would otherwise be working and increasing profit used to increase productivity etc etc etc. But if you kill them you reduce the labor force and thus drive up the price of labor, reducing your profits, and thus what you can spend on improving productivity? And other countries which didn’t do so would become more advanced, leaving you behind.
The ideologies are mildly opposed but not deeply. Capital profits more under liberalism. Making sure everyone has access to markets and the right to own property means that more people who can buy and labor within the system. If you go around killing off minorities you're also killing off potential customers.
Fascism is fundamentally opposed to communism, since communism seeks to remove racial and class divides, while fascism seeks to entrench all hierarchies. Capitalism is also fundamentally opposed to communism, obviously. So the ideologies agree that communism must be stopped, and that takes a higher priority to the capitalists than making sure they can sell things to the victim of the day.
Capitalism is also a system that puts large amounts of power into the hands of individual people, as a consequence of them performing a specific structural role in capitalism, rather than due to their actual understanding of capitalism and their role in it. The ideology of capitalist elites does not actually have to be capitalist, and can be anything else that's palatable to people who are placed under a position of extreme privilege. Many of the elites have other compatible ideologies like a fascist / great man theory / "right to rule" thing, or Christian prosperity gospel, rather than actually believing in capitalism. So inevitably many of them are going to choose to support fascism, even though that's suboptimal for the capitalist system, because they're fascists.