You know how most bathrooms have a fan in the ceiling? Do those actually go anywhere? Or are they just there to make noise to cover up farts?
It's like, I've never done this, but in a public washroom, if your friend has to go make a loud poop, you can keep the hand dryer running so nobody else hears it. I hear this is why girls travel to the bathroom in packs.
Or like, in my kitchen, there's a fan in the hood above the stove. You'd think it sucks air up into a vent that leads somewhere outside. But no, upon closer examination, it becomes clear that the fans just vent air out of an opening about an inch above the hood itself. All it does, then, is take hot air and scalding steam and choking smoke rising from the stove and spit it out a bit higher up; at about eye level. Maybe bathroom fans are kinda like that, except useful in their noise-obscuring abilities. The one on my stove not so much, because I rarely fart in the kitchen.
Actually I never fart, but that's a story for another post.
In conclusion: if a silent bathroom fan was invented, nobody would buy it.
Stay thirsty my friends.