Can you elaborate on how the S curve is being "antithiesed"?
The theory behind using (ideally few) simple curves (CSI) is called line economy. Simple curves can be used by the draftsperson in a very controlled way, and reducing the overall complexity of the form leads to very easily readable shapes that look pleasant. There are some minor caveats, like only using single curves ("C"s) on the whole figure, placing them symmetrical and have their ends always match, can lead to snowmansyndrom, where the body appears to be assembled out of a collection of elongated spheres, like a balloon animal.
I am not aware of specific problems with the S-curve, and use it a lot. The human spine, which is often the basis for the Line of action, naturally follows an S-curve when seen from the side in an upright posture, and S-curves appear all the time on various limbs.
I am by far not a master draftsman, but I think I can handle line economy decently well, you can check my results on my sketchbook here or on artstation.com/stefanbast. If you have concrete questions about line economy, I will try to answer them to the best of my knowledge.
Honestly I am not really well versed with gesture(starting my learning curve last month). But I saw S curve being disapproved on this article of this website. If there is something wrong with my understanding, then please help me clarify with this.
https://www.dropbox.com/s/cpmwrlwczzkev81/IMG_0042.JPG?dl=0 Is two different takes (by me) from that same reference. So yes, you can use an S curve. But for me, it's harder to continue with the sketch I started with the S curve. It's tougher to judge whether I got the curves right, and it's hard to add on straight lines where they should go.
The goal with the tutorial is not to give hard and fast rules. It's to point you to areas where it's worth exploring. So focusing on simple curves and straights, maybe trying a sketch that's all straights even if it feels like an S curve would be easier... that will teach you things. Or on an image where it feels like it's full of straight body shapes, try doing it with all simple curves, see where that gets you.
There's no objective wrong answers in gesture drawings. But there's answers that are wrong for you.