I was wondering, do dentists have to pull out cavities before inserting braces?

Sort of...: Cavities are "holes" in teeth, therefore, they cannot be "pulled out." a tooth can be removed ("pulled out") if decay is extensive. Otherwise, the cavities should be filled prior to braces.

Prior to braces: You should have your general dentist give you a complete exam and appropriate number of x-rays. Your teeth and gums should be in optimum health- no cavities and gums free of any inflammation. A good orthodontist should require this! once the braces are on, it's harder to keep everything clean and it's more difficult if not impossible to address these issues.

Yes: Infection must be treated before aligning teeth. It would be unethical to do otherwise. Ask your Orthodontic Specialist to communicate with your General Dentist to properly prepare your teeth for Orthodontic care.