My dentist wants to remove four teeth, only one is bad (photo)

it is difficult to say anything without seeing xrays . its my advice to upload xray so i can guide u better. in sever perio cases extraction is last and only option.

Extensive gum disease can affect young people. So, the decision should be made based on x-ray, and clinical examination, including a periodontal chart. Sometimes it is better to remove hopeless teeth to eliminate areas of infection and help you keep good hygiene. 

Without examination, pocket measurements and full mouth X-rays there is no way to give you a definitive answer.  Most dentists will do what they can to keep patients teeth as long as they salvageable.  Teeth that look fine on the surface can still have major issues that are not visible to the naked eye.  Bone loss can still occur around your good looking teeth and cause need for treatment.  Of if you are not sure about the need for your dentists treatment recommendation you could have here explain and show you on X-rays what is going on in your mouth.