“Secure in my/his/their masculinity” is a common expression, but what does it mean? Some readers may find this obvious, but permit me a bit of exploration, to see what we can learn.
In a basic search, I found several low quality listicles, which I take to represent what the common person thinks (as opposed to more scholarly interpretations). The listicles say that you can tell when a man is insecure in his masculinity if he tries to one-up everyone, is homophobic, or avoids anything girly, and so on. In short, masculine insecurity is evidenced by toxic masculinity.
The underlying theory seems to be that insecurity about masculinity causes toxic masculinity. And, by the way, this theory seems to be correct. Another article I found in a basic search describes psychological studies, where men were given tests of “masculinity” and physical strength. They received randomized scores, and the men who were told they scored poorly reported higher aggression, would exaggerate their height, and be more likely to avoid products perceived as feminine.