I do the class scheduling at my school (private HS) so in response to the earlier question: 99.9% of the time, I am just trying to get kids into reasonable classes for them with no regard for who is teaching it. I get requests from students and parents for this or that teacher but there are far too many other factors that take precedence.
Also, you might not know that private school teachers do not need any education training or certificates. And as someone who hires, I know that most of us think having a degree in, say "Science Education" is far inferior to someone with a degree in some specific content area, say Biology, and the person with education classes at college won't even get an interview over the latter.