
You're right, it's not reverse discrimination. It's discrimination.
Overall, the article isn't terrible? I mean, I disagree with the conclusion, but it at least shows some awareness that skinny-shaming is not ok and the author appears to genuinely understand that it's not so simple as to say "'reverse discrimination doesn't exist lol".
The main argument appears to be that fat-shamingis worse than skinny-shaming, because while they are both forms of sexism fat-shaming is at the intersection of fatphobia and sexism, and so it gets more Oppression Points. (the other argument is the standard your suffering is bad but it isn't as bad as this other form of suffering because it isn't Structural Oppression".
I don't think that's a productive way to look at intersectionality, and frankly the whole idea that we need to rank different forms of shaming from best to worst is rather dumb. The entire category of behaviours containing fat- and skinny-shaming is stupid. It's harmful. How much it hurts you depends more on who you are than anything else. Trying to say, "yes but this is worse In General because this structure here" erases individual experiences, or whatever the latest sj-buzzword for that is.
But here's the part that actually bothered me rather than just disagreeing with it. I tried to track down that article but the only version that exists right now is "
4 Reasons Why We Need to Stop Thinking of Skinny-Shaming as ‘Reverse Discrimination’"
If you track down
the old version, you'll notice the reason that got deleted is that "It Can Be Used as a Tool Against Oppressive Structures". In other words, "skinny bitch" is in the same category as "white devil", and apparently that's a good thing. Because if you throw it in people's faces they'll stop being so oppressive of fat people, somehow.
At least it's nice that they removed that, but it's disingenuous that they left no mention of it in the currently available version. A simple "Editorial comment: a previous version of this article blah blah blah" would've sufficed.