One can answer your question partly by recognizing that, in the 60 years since Look Back in Anger premiered, our ideas on what actually constitutes masculinity have changed. Jimmy Porter seems driven to express himself as a man through aggression and abusiveness. Though he's an educated man, he prefers to make his living running a market stall. There is, of course, nothing wrong with this, but one senses that Jimmy chooses it chiefly in defiance of his wife Alison's middle-class background. Thus, to him, "masculinity" is somehow demonstrated by independence from or resentment of his wife's values. Jimmy also lords it over his friend Cliff, who functions as a good-natured sidekick to him. This is another way of Jimmy proving his "alpha male" status.
At the root of these factors, and of Jimmy's contempt for (and subsequent seduction of—another demonstration of his "masculinity") Alison's friend Helena, is anger. Jimmy Porter, of course, is the archetypal Angry Young Man of postwar theatre. Various elements converged in the 1950s to create this phenomenon: class conflict, post-WWII economic factors and disillusionment, and resentment against the changing status of women in society. Jimmy's assertion of masculine values seems, from our vantage point today, a kind of caricature. To some extent, Osborne probably intended it that way, because even from the perspective of his own time, Jimmy does not come off very well. Far from glorifying Jimmy, Osborne simply reports things as they were, and in looking back on Look Back in Anger today, we can understand that the dysfunctional dynamic of the Porter household, unfortunately, is not totally a thing of the past.