SpinFree...personally, I find teachers can be very manly and very sexy, so I don't really get your wife's position. However...since she came out and told you this, you really need to listen to whatever her real feelings are. It could very well be that it is something else about your job that is bothering her than simply lack of manliness. Did she say any more specifics?
To be a real manly man about it, you should sit her down and say "hey babe, regarding your revelation to me the other night about how you have no respect for my new position, I'd like to open a dialog about it and get into your head a little bit. I'd like to know exactly what you don't like about my new job so we can see if there are any changes I can make, or if I am just doomed to be unrespected by you for as long as I'm working. I do care about your opinion, so I'd like to discuss this".
Then lead her into a conversation about it. If she will take the bait, let her ramble on about it for a bit while you nod and use "hmmm" and "umm hmmm" sounds. Just let her speak. She will likely at first start off with "well I don't know its just so this and that" and give generalities. She may not get to the root of her feelings until she's talked for a little while. But eventually if you keep prompting her for more information, she'll likely open up to the truth.
You may find out something really weird, like that her real problem with your job is that you are around hot young high school girls all day and she doesn't trust your eyes not to wander. I'm not saying that as an insult, but many young girls dress just too sexy and don't seem to have parents who tell them to cover up their boobs and asses when they are in public, and grown women can feel very anxious about this. Not that she is jealous per se, just that it may annoy her. Same as if maybe your wife were a college foot ball coach and spend time around these strapping young men all day, catch my drift? It may annoy you on some level.
Or maybe it is something else entirely, like what you actually teach in high school. Maybe you teach drama and she has never had any respect for that type of art.
Or maybe she actually does respect your position, but something else in your demeanor is what is bothering her. Maybe you are too close to your students in general and she feels it makes you behave immaturely (ie: talking about what music they are listening to or telling her stories that the kids told you when you get home).
If you don't know for sure exactly why she disrespects your profession, you need to find out. Make sure when you open this dialog that you don't act defensively about whatever she says. This is a fact finding mission for you at first. This is not your chance to defend yourself. It is truly getting into her head to see you as she sees you so you can then work within yourself to correct her view of you.
After she talks, take whatever hints you have about it with you for later personal reflection, don't respond just yet. Just thank her for her honesty, don't act hurt or mopey about it (no matter what she says or if it does hurt you), and tell her that as her husband, you will work toward gaining her respect because you deserve it and she deserves to have a husband she can be proud of. Then put the topic to bed for now. Don't bring up other topics, instead change the subject entirely or go do something else...but don't do any escaping...do something with her or something she cannot view as you escaping from what she said...the key is to appear confident and not mopey...like she can't hurt you with what she said. One thing that is very hard for a woman to do when she feels her man isn't being manly, is to try to tell him this and then he gets all hurt about it, which just reinforces her point in her mind.
Be prepared for anything she might say. Don't assume you know what is on her mind (unless she's already told you and you didn't tell us that in your post).