I am a woman, and pretty much every friend or acquaintance I have thinks that I NEVER cry (see below for exceptions). I was talking to one of my best friends last night (have known her for 10 years), and she was shocked to hear that I do get emotional about my relational struggles at times... she said the only time she had seen me even sniff back a tear was at my wedding. She thought I was a rock, very balanced.
Apparently I am pathologically good at suppressing my emotions most of the time, around most people... which is odd, given how VERY sensitive and emotional I can become when I am alone, or around my husband or parents (particularly my mother). It is quite the opposite, in that case... I will cry buckets upon buckets when I am alone, and if I feel either very safe or very angry/sad, I will cry with my husband or mother at almost the drop of a hat. But you will NEVER catch me doing that with anyone else.
In fact, I *cannot* cry in front of anyone else. Even in therapy, when I've talked about some of the most disturbing things in my life, it's hard for me to feel anything in the moment. I guess I see myself as being pretty tough in any situation, with just about anyone around... but around my husband especially, I become extremely vulnerable to any and all fluctuations. It's very puzzling, and frustrating at times.
As for my husband, well from my point of view, I have always found it so intimate when he has been able to cry in front of me. I would never say that he should "cry for me" (as your SO said)
since it's really a very personal thing... but it really brings the intimacy level to another level when you trust someone to that degree.
Despite my inability to cry around most people, I have never, ever seen crying as a weakness... I really admire when people are able to express themselves so sincerely and honestly in that manner, because I see it as them finally overcoming the social programming/trained response that forces them to keep it all inside. I always embrace that kind of thing in other people... perhaps because I have such a hard time with it, myself.