Strange, I was taught that sex that determines whether a sexually reproducing organism produces male or female gametes.

You're describing anisogamy. Large males are sexually selected for in elephant seals because they can fight off other males, but small males are sexually selected for in spiders for they can mate with the female quickly while avoiding being eaten.

They said larger gamete, not larger adult size.

Huh, is this actually universal? I'd have guessed there'd be at least one or two exceptions.

There are no exceptions to it if you make it the definition. Which is what the comment of BuyMyBitcoins says was taught to them.

Yep, fair enough, if it's a strict definition. You could potentially then have weird edge cases in the other direction, though; if the same sex chromosome layout in related species X and Y leads to different sexes due to the size of the gametes (especially if the size of the gametes was pretty similar to start with), that seems very odd/confusing.

It looks like there are cases where the size of the gametes are identical. But when this happens they don’t refer the organism’s sex as “male/female” and instead use “+/-“. https://en.m.wikipedia.org/wiki/Isogamy

Going a step further I found this: >Depending on the group, different mating types are often referred to by numbers, letters, or simply "+" and "−" instead of "male" and "female", which refer to "sexes" or differences in size between gametes. https://en.m.wikipedia.org/wiki/Mating_type

So it does seem to be a strict definition and anything outside of the strict definition is given an alternate identification scheme.

Here's a fun edge case: https://en.wikipedia.org/wiki/Indotyphlops_braminus#Reproduc...

All individuals of this snake are female (presumably 'female' here is defined relative to other snakes) and reproduce parthenogenetically (sic?). By your definition, these wouldn't have a sex at all, presumably.

A closely-related species using the same or similar chromosomes, where male/female exist, is likely where it came to be that the observed individuals of these snakes have all been determined "female", even if no "male" has been observed.

And that's the definition used in the article. (Where "egg" = "larger gamete")