And that is ONLY because we've been socialized differently. There is zero "core" difference between men and women. While I agree that nobody should be telling others they "ought" to do something, it is still vital to counter hundreds of years of pressure for men to stuff their difficult emotions and to normalize learning to express them in ways that are fundamental to human mental and emotional health.
This isn't a "woman" thing - it's a basic psychological precept and all sorts of organizations run mostly by men have pointed that out. I do like your suggestions for making yourself available to support him and letting him take the lead on how he wants that to take place though. I don't know anyone who can authentically cry on command.