You might start with a few pictures - say Alex Drummond (a TW on Stonewall trans advisory board).Is Alex a woman? If your colleague thinks so, then why? What makes Alex a woman? Should we treat Alex exactly like a woman in all situations? Would that be fair? How would women feel about it?
You could talk about Stonewalls definition of 'Gender' (below):-
Often expressed in terms of masculinity and femininity, gender is largely culturally determined and is assumed from the sex assigned at birth
and 'Gender Identity' below:-
A person’s innate sense of their own gender, whether male, female or something else (see non-binary below), which may or may not correspond to the sex assigned at birth
And then check out the Wikipedia page on femininity which includes:-
Traits such as nurturance, sensitivity, sweetness,[15] supportiveness,[11][8] gentleness,[8][9] warmth,[11][9] passivity, cooperativeness, expressiveness,[25] modesty, humility, empathy,[8] affection, tenderness,[11] and being emotional, kind, helpful, devoted, and understanding[9] have been cited as stereotypically feminine. The defining characteristics of femininity vary between and even within societies.[11
Stonewall are saying that a woman is someone who 'identifies' with the set of characteristics above. Loud, boisterous, assertive, ambitious females are not women, apparently.
And then ask them how this is not about old fashioned regressive stereotypes used to hold women back from time immemorial.