I'm not sure if you realize that it was me that you were replying to elsewhere in this thread, but I think you actually answered own question. In a vacuum, it shouldn't matter, but in reality, it does. When "randomly" picking who coordinates social events, or work happy hour, is it generally a woman? When you're talking about introducing a new idea in the office and you check with a colleague, is it always the same sex? When someone at work asks for a moment of your time, who are you finding immediate time for? I'm not saying that you have a gender bias, I am just saying that society has a gender bias, and often people don't realize their subconscious gender bias. If you're not paying attention, you can definitely fall into societal assumptions about gender without even realizing it. Heck, you might even find that you are white knighting, and helping women more than men. Maybe you never fall into those issues, but most feminist theory thinks it's important to be at least conscious of this sort of thing.

I kept it mostly work related, because interpersonal relationships are all different and I don't really know anything about you or the kind of interpersonal relationship you would have, but it generally applies to those as well. Obviously, the work examples are also quite specific for a specific kind of job, but hopefully it gives enough of a picture that you could extrapolate how unconscious bias could affect all kinds of jobs and not just insert sitcom office job here.