Ok..ok. I think I have a simple answer as to why the president gave off that pheromone that the mc thought was an alpha pheromone.
There's the simple fact that sister's pheromones possibly stuck with the president since the family does live under the same roof. You know how people smell just like their house? An alpha's scent is said to be strong and obvious, at least obvious to omegas and even other alphas. Betas cannot tell the difference. There's the possibility that because the president identifies more as a beta than an alpha theres the chance that she never noticed that she must smell like an alpha. Even if she is a "defective alpha" and possibly does secrete her own alpha scent at a subconscious level, even if that ever was the case, the proof that she technically doesn't is when her and the mc first met and the mc's heat triggered. An alpha, and even a defective alpha, should've sense the pheromones of an omega. Hell she's been in that school and no other omegas heat had triggered around the president. Sure maybe the other students around her are betas, but its a school of betas and omegas. The president is in the school because she's not an alpha! What school would risk their students going into heat around a single alpha!?
The point is that an alpha scent is strong, like just an alpha being around another individual can leave that scent on them. Meaning this whole time that the mc thought it was the president's scent was the president's sister's scent this entire time. That's why the mc reacted the way she did and the president had a complete lack of reaction. If the president really was an alpha or even a defective alpha that instinctual side of her should've reacted no matter what.
Basically concluding that the president isn't really an alpha.
She doesn't give off an alpha scent.
The pheromones on her are actually her sister's pheromones.
The mc fell in love with the president due to the president's sister's alpha pheromones. BIG FUCKING YIKES.
Oh man I definitely can relate. Gender dysphoria ain't fun to deal with at all, 'specially if you dont have a support group and without anyone there to even just listen it gives that feeling like if the world is against you. Good thing he still went to get the surgery after that talk with the dad cause the amount of anger, sadness, dissapointment, and most of all the dysphoria I felt from that scene... I've been there too so I get it. Thankfully I've gone through hrt and I'm now a happy, bearded dude with so much to look forward.
Also Takatou is like the most supporting friend I ever seen. The true mvp of this story.
Was finishing up my beer to go to sleep until I noticed this gem. I'm genuinely surprised that someone actually drew in manga format an omegaverse. It's actually not bad at all, and thats coming from someone who reads too much omegaverse fanfictions.
Also for those who are new to the omegaverse this type of story, 'a weak alpha and strong omega' is a little uncommon but it's completely possible for there to be this kind of situation in the omegaverse. Typically alphas display acts of confidence, strengh, aggression, (basically "toxic masculinity" as some call it), ect. While omegas display the complete opposite of an alpha, like being quiet, having consideration to others, not being the center of attention, etc. These traits are things that children in the omegaverse will display but wont actually know what they are yet until they either reach maturity and get tested or give off a distint scent. Btw alphas have a musky scent while omegas give off a tantalizing sweet scent that drives alphas sexually insane. And in the omegaverse female alphas can have a penis (or not, depending on the writer) but this is usually the case when it comes to female characters paired up with other females (for mating/breeding purposes).
Also at the end the sister mentioned she wanted a temporary mark.. A mark ain't just a mark or a hickie, well not by itself at least. A mark in the omegaverse happens when a pair mates and the alpha bites an omega (or beta) around the neck near or on the scent gland located near the pulse of the neck. Usually the bite happens when the alpha is about to climax, thats the time when the hormones and the scent are at its strongest. And when that happens the omega will have the scent of an alpha for a while, thats in order to alert anyone around that the omega is claimed by an alpha. So in other words, in this story there's not way in hell that the parents wont find out!
The whole "real friends" situation definitely felt like a punch to my gut for how real and similar that type of bullying was for me during my youth. But honestly I'm glad the character picked the better choice of not sticking with fakes and found happiness later on.