Suggest Treatment For Tomophobia

I'm getting my wisdom teeth removed soon. The dentist told me that they won't be using a general anesthetic/they won't be putting me to sleep for the procedure. All of my friends say that they were put under, and I'm only getting a local anesthetic. I have a very specific phobia that I'm worried this surgery will end up provoking, and I'm super nervous.
So my question is, why wouldn't I be put under when I get my wisdom teeth removed? I want to know so I can decide whether I should ask for it or not.