the thing about the word
"gender" is that it's stupidly confusing because it can mean like three or four different things depending on the context. the definition you gave is the sociological definition, but it can also be synonymous with biological love, gender identity, or even grammatical gender. and i know someone is going to say that's just because of the tumbler sjw hijacking the english language or something; this definitely isn't a distinction that's always been very clear, academia in sociological studies and natural sciences has over time found increasing usefulness in this distinction existing, and so throughout the 20th century that's the model that became more prominent. it isn't a recent phenomenon by any means, it came about because it helps us to better understand people and societies by understanding how our biology affects our internal and external experiences. it's not a distinction that came about just to validate people's feelings, it serves a highly utilitarian purpose
so it's better not to split hairs about definitions since there could be several; that's probably never the core issue anyway, at the most it should only be necessary to clarify what definition applicable to a specific statement
