...are related. In many cases, one causes the other.
Yes, there are some men who get uncomfortable knowing that the woman in their lives brings in a bigger paycheck and it threatens their self-esteem. They're a portion of men.
However, an even greater portion of men would flat out stop being bothered by their girlfriend making more if the average woman was not so hung up on how much her boyfriend makes to begin with. If most women did not care about a man's income, most western men would not get bothered by the issue at all. It could even become an accepted norm. The fact that many woman DO consider it a standard issue is part of why many men are "intimidated" about falling behind. Because the women they want to date will literally penalize them for it...
Them being related is part of the point that I'm making. The landscape has changed a bit over time but I'm not so sure that it's mainly due to women making their SO's income an issue. If a guy has a patriarchal "I must be the provider" mindset, he's likely to have an issue with it regardless because he wants to feel like he's the main one doing the providing. As long as women are expected to deal more with the home and kids, I'm not so convinced that them ALSO earning more money is likely to become the accepted norm. Men are going to have to be more willing to take on some of more traditional gender roles of the opposite sex.
I'd wager that men's desire to be the primary provider has more to do with women's disrespect and disregard for men they outearn. As has been mentioned, women don't tend to want to mate down, which is probably what puts pressure on men to want to be the provider. Women largely still want men who are above them in the social ladder and are loathe to settle for men under them.
I agree that it plays a role but I think the provider thing is ingrained in society regardless. I'd say one of the main reasons for women not wanting to date down is because of the idea of men being the provider. If a woman has it ingrained that a man is supposed to be a provider and take care of her, and the single biggest way to do that in society today is through money, then it makes sense for them to only want to mate with dudes that have more than them.
I don't think that role of men as provider is an issue of social conditioning. I suspect its biological inclination informing how our societies are constructed. At best, I think, you could say that, because humans are tribal animals, our social pressures reinforcd those natural inclinations.
I mean, men mostly being most of the heads of households, primary providers, leaders, etc seems to be pretty standard across various cultures. Seems unlikely that would be a coincidence if that kind of structure wasn't ingrained in us as a species.
Totally hypothesizing here, but my suspicion is that in the early days of our species, women needed men to provide for them, because a pregnant woman is going to have a much harder time providing for herself in those harsher times.
So, women who were inclined to depend on the men to protect and provide for her and her offspring would have a better chance to pass on whatever genes predispose her to feeling a need to depend on men. For similar reasons, men evolved to tend to be bigger, stronger, and more prone to status-seeking, risk-taking, and aggressive behavior than women.
I don't think that its society that teaches us that. I think that is the type of behavior you'd naturally see in humans and that you'd need a society to train people to behave differently from that.