So all animals are in different species to members of their same sex?

I'm joking a little of course. But only to make the point that the definition of species taught in high school is very difficult to pin down. You identified one way. Even more common: not all organisms reproduce sexually. But also: some organisms (protists) perform sexual recombination separately to reproduction. And even for well known higher mammals (which is where the 'offspring must also be fertile' clause comes from), 'fertile' is by no means binary! A sexual definition of species is simple, but rather difficult down in the nitty-gritty.

It is always worth bearing in mind that species is a human classification concept, not a biological reality. It's not surprising that it has very grey edges.