For everyone
People ask me this a lot, and there's more than one reason.
Tutoring and teaching are different jobs
A classroom teacher has a fixed amount of material to cover by the end of the term, and the department expects all of it covered. That's why so many math classes speed up toward the end, sometimes covering a whole chapter on the last day before the final.
It often happens because the class came in without the foundations the course assumes. The same question gets asked again and again, and the answer only makes sense with material from an earlier course. A teacher can't reteach that in the middle of a lecture, so the pace slows, then the end gets crammed. This is also why colleges give placement tests. Many students, with the best intentions, place themselves into Algebra II without being ready, hoping to buckle down and pass. Most of the time it doesn't work.
A tutor works differently. Students come to a tutor because they want help, and the tutor answers the questions that student has. I work with one student, or a small group, and can focus exactly on the difficulty. I have no syllabus to rush through. I can go at the pace that fits you.
What I'd rather spend my time on
Schools come with plenty of bureaucracy, and that isn't where I want to put my energy. I also don't have the master's degree community colleges require. I could petition, but I'd rather spend that time with students. High-school teaching isn't for me either: I love teaching math, and I'm happiest with students who have chosen to be here.
Tutoring gives me a flexible schedule, simplicity, and control over how I work. I doubt teaching a class is in my future, but you never know.