I'll be honest - I like "mean" teachers! Although I hated them at the time, I now see the benefit. This doesn't include abuse, which there is 0 tolerance for, but some teachers are just "over- the-top" strict, which can be just fine.
Setting the bar high on being orderly will exercise areas where children are naturally weak.
Kids will learn how to manage adversity.
If your kid can make it with a "mean" teacher, they can make it with anyone.
They learn that "Life is not always fair."
Of course, if the teacher is emotionally abusive (name calling, belittling, humiliating) then investigate it further. Most of the time it's really the kid's fault and they are just blaming someone else, but just one case of a teacher being abusive is intolerable.
"So how do I know the difference?"
Is this teacher being reported by others? (If they really are that bad, they will have a history.)
Does your kid seem genuine, or are they just avoiding fault? (You know your kid, would they make this up?)
Is your child having a damaging consequence that they honestly didn't earn? (Low grades, removal from activity.)
Summary
The term "Mean" implies abusive, but it could also describe being strict.
Know the difference. If a teacher is just really strict, then by all means, go with it - But if a teacher is being cruel or abusive, then call the principal and schedule a meeting to discuss.