When you go in for a tooth or teeth that you want pulled the dentist will want to see if they actually save the tooth or teeth first through dental care.
Sometimes the tooth can be saved and the tooth infection can go away with dental treatment so they want try to save the tooth first.
Having your real teeth is a good thing and dentures or even dental implants are not the best so if you can save your natural teeth which are best it's better for you.
Pulling teeth is pretty safe but it can also be dangerous as the dentist needs to cut at the gums and bones to actually safely remove the tooth.
So it's more involved than just yanking the tooth out.
You can have the tooth pulled if it's really what you want to do but you may have to go to more than one dentist to get the tooth pulled when you really want it pulled.