You're right after that comes the patriarchal, or just gendered, double-whammy: Women culturally do have more of a support network, even just in the "friends hanging out" way, as the male "do things together, chop wood, go fishing" is regarded as work, not leisure, and thus co-opted by capitalism: "What do you need to chop food and fish for, go buy fuel and food are you poor or something". Thus all the productive time men have is spent in a hierarchical worker-boss environment, never "pals doing stuff", cue loss of connection, alienation from broader society, loneliness. Going bowling? Time not spent hustling, you're a loser. That's your mind on patriarchal capitalism.

Thus, even if the starting conditions inflicted by capitalism are, for the sake of argument, completely even, it still hits men harder when it comes to loneliness. Women are more affected in other ways. This isn't an olympics, it's analysis of the material conditions we live under.