Beutner's stance throws into question whether schools will be able to reopen this academic year.
Right now vaccines for teachers aren't available, except in the city of Long Beach which has its own health department.
Los Angeles County health director Dr. Barbara Ferrer said Monday it will be some time before vaccination distribution is open to teachers.
She noted there are more than 2 million people in the first priority group to be eligibile, including health-care workers, residents over age 65 and residents of congregate living facilities.
With two doses each, that's more than 4 million vaccines being distributed before eligibility is expanded to other groups such as teachers.
In the meantime, the teachers union is pushing things one step further saying they also want to see infections drop significantly before returning to classrooms.