I'll disagree with Kayty here, although it is something I just thought about this week. Look at the photo below:
Historical note - the rider there was later killed in a gunfight in a saloon. Don't know if he took offense to someone calling his riding a chair seat or not.
But while his heels are forward of his hips, that is NOT how someone looks sitting in a chair. Now compare my youngest daughter and I:
She has a chair seat. Her thighs are almost parallel to the ground, like sitting in a chair. In her case, it is caused by her insisting on riding a saddle that is too big for her. My heels are a bit in front of my hip, but my thighs are about as vertical as the saddle will permit (and parallel to the poleys).
There are a couple of important differences. When your thighs are parallel to the ground, you aren't using them to glue you to your horse. They are mostly sitting on top of the horse, like a piece of luggage. They also mean your center of gravity is higher, and the higher your CG, the easier it is for a fast turn to dump you. If your horse needs to spin, your legs are getting in the way, and your weight is like being in a chair spinning around with your legs out instead of in - you spin faster and better if your weight is carried in a vertical line.
My heels may be forward, but most of my weight is being supported by my thighs. The friction of my thighs helps when Mia goes from trot to the "OMG Crouch" - like today, when she saw an ENVELOPE sitting by the road! OMG! Keeping more of my weight lower on the horse helps when she jumps sideways. But heels forward also helps me get my thighs down. My hips won't spread far enough to allow me to get my thighs down if my heels are under my hips. Instead, that forces my crotch out of the saddle. And that hasn't changed any in 4.5 years of riding. Heels a little forward also help me get my heel down, which is good, and to do it with a relaxed leg, which is good.
If a chair seat is defined as 'heels in front of hip', then I will always ride with a chair seat. But I think a better definition is that a chair seat is when your thighs are parallel to the ground, like they are in a chair. THAT is harmful to riding no matter what style of riding (except racing horses, where you accept it in exchange for getting every bit of speed from the horse).
My daughter can get away with it because she ONLY rides a forgiving and very good-hearted gelding. If she tried it on my mare, she'd be dumped. In fact, she DID try riding Mia once for a lesson, and Mia threw her a minute into the lesson...
My daughter still doesn't listen to me about riding, though.