Wrong. You could redefine half-elves in terms of something other than sex. I think one good use for them is for fey-touched humans. In fairy tales, there are stories of people taken to Faerie who later return and are out of place in the human world; there's also stories of fairies stealing children and replacing them with changelings, which tends to focus on what happens to the replacement instead of the fate of the child. What if the child is raised by elves, and returns as an adult? The result is a freak: a human being who doesn't act human, who might even be referred to as a "half-elf" by townsfolk.
It's a tempting redefinition.