Why do they need to be able to reproduce for their sex to count?

They keep happening, even if they don’t have children. It’s just a fairly common mutation.

There are plenty of genetic conditions that aren’t hereditary. Like Down’s Syndrome for instance.

See, I think you may just need a dictionary. Binary means there is one or the other, there is no “both or neither” option. If you have more than a forced “either/or” choice, then by definition it’s not binary.

True, false, and neither isn’t binary by any definition you’ll find in any dictionary.