My marriage counselor seems fairly tuned in to emotions (except for a bit recently maybe...), but he's said he's had a lot of therapy himself. Plus he's married and has a teenage daughter, so I'm sure he's used to dealing with female emotion in his personal life.
It seems good that your T wants you to help him understand...but odd that he would make that distinction between men and women. Though when I'm depressed, for example, I tend to get weepy and down on myself. After my husband's close friend passed away a few years ago, he just seemed to be angry all the time, taking it out on me and our daughter (just verbally, thankfully). We later, in marriage counseling, realized that he was probably grieving and depressed, but it showed itself differently in him. Though I don't think it's a strictly male/female divide--I've had a male friend as well as an ex that tended to be weepy...plus a female friend or two who tended to get angry and defensive. Maybe your T is just trying to understand you.