So sexism, like any form of discrimination, doesn't just come in shocking bright red, "hey honey, why don't we go into the copy room for some hubba hubba". Rape can be a sexist act of violence, that's an extreme. Just because that extreme exists doesn't mean that less obvious forms of sexism and discrimination aren't ugly and evil.
A really pernicious dirty disgusting thing about sexism (and racism) is that it can be subtle, and hidden, and still hurt people. Pay rates, job discrimination, advancement are examples. Pressure to conform to a feminine ideal or be see as "bitchy" or overly aggressive.
So yeah, that's one bad thing. There are plenty of bad things. And sexism is bad for your business. Because discrimination doesn't just mean that some people are privileged over others. It means viewpoints, ideas, projects etc. from people who are women are not given the attention they deserve not because they are lacking, but because their source lacks testes. Discrimination doesn't just hurt women, it hurts everybody.
You advance a guy over a more deserving woman... you are hurting your business. sexism is suboptimal. It doesn't even have to be that obvious. You make a person feel unhappy or uncomfortable at work and the work their team is doing will suffer, if only because of the communication problems that arise.
Even if you aren't sexist (and it's hard to be a hundred percept free from stuff like that) sexism still informs the industry. The things you do that contribute to you being a programmer are often informed by gender roles and expectations. Math class for example.
Anyway, I recently came up with a test for sexism. It's a test I fail, but it makes me think. Ask yourself, is it better for something, a hobby, a sport, whatever to be manly or womanly?