I'm pretty sure men have anxieties too, or at least phobias. I know men who avoid air travel if at all possible, and it's not out of concern for their CO2 "footprint". My own phobia is heights. It's gotten worse over the years rather than better. But it rarely gets in the way of my doing things I enjoy. If I were getting deflected from something I truly would miss doing, like say biking, I'd do something about it. Mine keeps me from hiking some routes, but I'm not in shape for those anyway and there are enough routes I enjoy that don't challenge my fears that I haven't really had to change activities.

There are courses for some phobias (air travel, spiders, ...). I don't know if biking is among them. Most involve simply getting used to the thing bit by bit, and building up positive associations while you're at it.

That was why my suggestion of finding a biking buddy for outings such as to a cafe or park. Wouldn't have to be a serious biker. In fact, maybe preferably just a friend new to biking herself. Last time I confronted my fear of heights was on a hike with DH, DD and DD's SO. They're all great hikers, so they were no help. What helped was running into another lady with a height problem a tad worse than my own, and the two of us offering one another mutual encouragement (including noting that at least part of the problem was the dizzying effect of our progressive lenses).