A dentist can pull out an infected tooth but they will likely first want you to take some antibiotics before the tooth extraction to kill off bacteria that could cause further infection when the tooth is pulled.
Then dentist may even have you take antibiotics after the tooth extraction as well.
A dentist won't always pull the tooth right away at the dentist appointment but instead they will usually take X Rays and look at the tooth and then if possible schedule another day for the possible tooth extraction.
Dentists want to be very careful when extracting and tooth and will usually try and fix the infected tooth first before extracting it.