Okay, sure.
It starts with the title. "How to teach your girlfriend programming" immediately tells women that this article isn't for her; it's for her boyfriend, so he can teach her.
The rest of the article regularly enforces this exclusion. He's talking to men.
Almost every time he refers to his girlfriend, he says "my girl", which, in the context of a professional article, is belittling. He says "my girlfriend" twice. Never does he say "my partner", which would have made the article much more inclusive.
"Every one of them told me they don’t want a programmer girl, they said they would go crazy. But I call that bullshit. It was just their fear talking."
There is so much wrong with these sentences. Why say "programmer girl"? They are women who don't want to be programmers. Saying it was their fear talking, and calling it bullshit, invalidates these women's legitimate concern for how the people in their lives will view them if they go into this field. Their fear isn't bullshit, the expectations of our society are bullshit (for the record, a lot of expectations made of men are bullshit too).
"What’s really everyone thinking is that it is impossible to find a girl who would be good looking, intelligent, interested in programming, and above all else, interested in you, the socially awkward geek. What are the odds of getting all of that?"
This whole paragraph reinforces the fact that the author is speaking only to men. Which would be fine, if not for the fact that this is totally relevant to women as well, with partners of any sex. It's not difficult to tell your own experience, a perspective of your own gender, and relate it to everyone.
"But let me tell you a secret brother, she doesn’t need to know all of this stuff. Everything in life can be learned."
Here again. How can you not see this?
"You can explain pointers, manual memory management, stack & heap allocation, garbage collection and much more in just a couple of hours if you chose the right metaphors."
So women can't understand these concepts without metaphors? Come on, man. And yes, he is talking about women, because it is expressed over and over that this article is for men, and it's about their girlfriends.
"But what if you had knives and wanted to teach your girl how to sort them (obviously by size)? You might have to do it two or three times for her to really believe you that it works, but the algorithm itself is stupidly simple."
What the fuck, dude. Sorting knives? The kitchen is aREALLY bad choice of setting for your first example of what a girl might want to program. Oh and don't forget that it might take two or three times for her to believe that you've done it. Sexist.
"It will be easy for her to understand once you find the right metaphor."
Sexist.
"The biggest obstacle here I would say is breaking the I would never understand that fear."
Invalidating, demeaning.
"to make some animations on her personal website that I made."
There is no reason to tell us that he made the website for her. It's a small thing, but it reinforces everything else. Mentioning it in this article is just unprofessional, and makes his girlfriend seem like a bimbo who couldn't do it herself if she tried.
"Basically I’m able to take what I know, extract the important things, throw away the 99.5% of wasted time on figuring out what is important and just teach her what she needs to know."
Her, she. More reinforcement. At this point in the article the author seems like he's trying to impress, and he's doing it at the expense of his girlfriend. He could easily have changed his language to reflect a more sincere and inclusive article. I will illustrate this by editing that paragraph.
"Basically, you want to convey the important information, and avoid the time that would be wasted for someone figuring this out on their own. Teach only what needs to be learned."
Personally, I disagree with his teaching method, but at least now the language is constructive and inclusive.
Look, I could cover the rest, but I have to go to work, and I'm sure you get the point. Remember too that all of this is caked deep in the historical and current context of the exclusion of women. I'm not saying the author is a terrible person for writing this, I'm just pointing out that his language excludes women and implies their technical inferiority.
And so it's sexist.