I didn't read the whole article, but just reading the paragraph, the idea appears to be that boys compete to make up for their feelings of insecurity. Note the sentence says "their OWN insecurities". So it's not talking about insecurities felt by the world, or insecurities that the world imposes on boys, but about insecurities that the boy feels himself.
I think "protect" is a poor word choice here. "Protect" means to defend or to shield. But the boy is not protecting his insecurities. If taken literally, that would mean that he is working to insure that his insecurities are untouched, that he remains insecure. What I think the writer really means is that the boy is trying to protect his own feelings despite his insecurities. He is trying to overcome his insecurities. Maybe "hide his insecurities" as you suggest.
(Note I am not commenting on the substance of the article, but just on the grammar.)