I'm not going to question the term has been thrown around poorly in arguments; it has and it shouldn't. It doesn't stop it being a useful tool that people discard far too frequently.
Privilege as a term is designed to make people aware of where their benefits might make them unlikely to notice problems. It doesn't mean they're better than everyone, and one privilege isn't the be all and end all of comparison. As so frequently pointed out, some starving African children are able bodied, but they're really not doing great. White, middle class males don't get literally everything either, but they have advantages and disadvantages in ways they're not aware of.
I can walk around and I have no issues with getting around London, and as such I don't really notice when a place doesn't have disabled access. I'm privileged because I don't need to notice this kind of thing and I don't know what it's like when someone refuses to make somewhere accessible because it's too expensive, or not structurally possible, and I don't know what it's like to have that life.
This doesn't mean my opinion is invalid if I said "Hey, that building doesn't have access, but it totally should. What gives?" and it doesn't mean it's invalid when I say "It seems pointless to have disabled access there; it's unnecessary and far too expensive. Why not this instead?"
It is unlikely though that I'll ever be in a position where I can explain what's difficult about life in a wheelchair though, 'cos I don't live like that. There's gonna be a load of minor things that I never thought about, and to say "Well I know what it's like, and I think if this happened it would solve your problems" IS patronising. Sure, I might have done the research, studied it for years, and I might _genuinely_ know what would help. It's just straight out unlikely, and when people say certain things, the fact that they were privileged in this way shows.
I'm not privileged in the fact I'm transgender and that's pretty difficult some of the time. My life isn't shite because of it, actually being white and middle class has made some of it a breeze in ways that other people aren't so lucky to have. One of the key issues is that going to the bathroom is a big deal - most places have one gender or the other and going in the boys results in bad things and going in the girls also results in bad things.
To me, most people are privileged in the fact that's never a thought to them. Don't make 'em better or worse people, just means that it's a bit easier for them for that particular bit of life. There's a lot of little things there that you won't think about, so when someone speaks up for me and says "The issue that Transgender people need solving is X", without asking someone living that, it's a bit weird. Yes, the NHS queues are terrible and that'd be nice to have solved, but in reality what I would prefer at the moment is a standardised manual for transgender patients so that I know if my rights are being violated when a doctor insists I have to strip down. Again, your views aren't invalid, it's just difficult for you to speak about and frustrating when my views are shouted down when it's something so personal.
Returning to gender, there are a lot of things you won't notice because you're male. That's not your fault, privilege was never meant to be about blaming people for things. It's just that it is easier for men to get onto these STEM courses, as you say, but not that it's the easiest thing ever.
Rich White Men don't go out of their way to prevent women getting on the courses - no one is suggesting that for a minute. The article, and I've only glanced over it, seems to suggest that men select men for these jobs without considering that they're being sexist, it's just inherent. There's a few articles on the internet about Academic sexism where they submit two fake students for the same course, same credentials exactly, just different gender. The women are less likely to be accepted.
On the streets, black men get random stop and search more than white men. We're not going out of our way to blame white men here - all we're saying is that there's a problem, and it's not obvious to you if you don't live it.