I think this question is never asked, but rather assumed. When you think of the word "teacher" what comes to mind? I would be willing to bet that it's a person who is in a classroom of some sort, with a couple dozen children sitting at desks. She or he spent years in college learning to be a teacher and has a piece of paper to prove that.
Am I close?
Here's is the definition I found in our 1926 Webster's Dictionary:
Look at definition one, "One who teaches, or instructs; especially, one whose occupation is to instruct; an instructor, a tutor," this is the one that applies to our discussion.
In the definition above, nowhere is it mentioned that one must have a college degree and credential in order to teach. But why? Even here in California, the definition of a teacher in a private school is of "one who has the ability to teach". Many of us homeschool in this state as a private school. It's only in the public schools where credentials are required by law.
So the vast majority of teachers out there probably don't have a credential, many have degrees but many others may not. That ceramics teacher down the street who teaches your kids how to make the most beautiful pottery; do they have a credential? A degree? Did you ask to see proof? No, you simply found out whether they could do what they said they could do.
All this comes up because it is "back to school" season for homeschool and public/private schools alike. Many homeschoolers right now, are out there buying supplies for their kids, many have one income, and are trying desperately to be able to financially afford to give their kids the education they feel is best for them. They often don't have an ID, or any "proof" that they are homeschooling, yet they are teachers. The stores ask for some sort of "proof" that they are teaching. Some of these moms and dads are just starting this year, and hear that a store offers "teacher" discounts, only to hear from some employee that it's only for "real teachers, with credentials".
I'll point something out: We homeschoolers pay into a public school system that we do not use, and by any definition is failing the students, then go and purchase curriculum and supplies to use with our kids.
To companies out there offering teacher discounts: Do the right thing and offer them to homeschoolers too, and tell your employees that this is offered. Often the new homeschoolers don't have any form of ID, in California we don't even file affidavits until October so we have no "proof" of being a school or teacher until then. These new homeschoolers have no idea that you're going to ask for "teacher ID", and just walk out feeling let down and abused by uneducated staff. You often lose customers over things like this, even though many of them will never tell you. They just won't come back.
So what does a teacher look like to you?