First of all, I think you're confusing your basic terminology.
Finance is the study and practice of the management of money or “funds” management. Meaning, if you have $100, how do you handle that $100 (up until you decide to spend it).
No, teaching most of finance is generally useless beyond very small basics (balancing a budget, inflation, concept of investment) - which really is included in economics (see below).
What you probably meant was teaching Economics, not finance. Economics can be defined as:
Economics is the social science that analyzes the production, distribution, and consumption of goods and services.
Basically, pretty much ANYTHING you do that relates to other people is underneath it an economic interaction. You going to work, performing work in exchange for pay. You going shopping and exchanging said pay for something you want to buy.
Please note that economic activity is really ANYTHING, not just money.
"I will help you move this couch if you let me watch the game on your new big screen TV". You got it. You just entered into a verbal contract in a non-monetary economic transaction.
Or even something that you don't think as an economic activity or exchange. "I will plant some flowers in my backyard because they are pleasant to look at". You gain benefit (pelasure) at a certain expense (work/time/materials expended on planting and taking care of plants).
Please note that a LOT of economics underneath is just game theory.
My history teachers were always the people I looked up to the most. I felt that they had a handle on the political world. ... when a school doesn't have a finance program, why don't history teachers pick up the slack?
Depends on a teacher. A large portion of teachers in USA are extremely left leaning politically, and don't have a handle from the point of view of someone who doesn't share their politics. More on-topic, people who lean left very frequently have VERY poor handle on economics and therefore can't teach it well.
Want an example? If you're left-brainwashed to think that somehow the USA represents the worst of human society because of "gap between haves and have nots" or some other OWS talking point, you need to first go talk to someone who lived in the workers paradise of Soviet Union and knows the difference between how Communist Party bosses lived and regular people. Hint: they will laugh at you, very long and hard. And then ask that left wing person (if they are old enough) why didn't THEY emigrate to USSR or Cuba if capitalism is soooo bad and workers have it so good under socialism.
Now, ask them to explain the difference between "unproductive speculation that should be prohibited" and "investment" that should be heavily taxed and their own pension plan holdings (that are all over the sudden not such a big evil). Hint: from both finance and economics point of view, they are principally the same, differing only in technicalities and who is the person benefitting (that teacher or someone else).
Another example: Ask any left leaning teacher what their view on minimum wage is. You will probably hear the standard left talking point (without it people will be evilly exploited, it's absolutely required and should be raised etc...).
What the DON'T tell you (and likely don't know) is that:
Raising minimum wage doesn't simply cause people to get paid more. It actually destroys jobs. So, if you only have the skills to do something that is worth $4/hr to my company, and you get paid $3/hr, I can hire you, pay you $3, and make $1 in profit (evil greedy me!). Now, if some nice politician comes along and decrees that minimal wage MUST be $5, guess what happens? You still can only do the work that is worth $4/hr to my company, but if I keep you employed, I will lose $1/hour on that. So the only thing I can do is fire you (and the reason you were working for $4/hr is likely because you couldn't get hired anywhere else at $5/hr, so they won't hire you at $5/hr now either). Well, the other option I have is keep you employed at a loss, lose all my money and go bancrupt - which will not only lose your job but everyone else I employed. Who's better off now? Definitely not you, Mr. minimum wage employee who now has no job at all. By the way, any study will show that this is EXACTLY what happens (# of minimum wage jobs contracts with the raise in minimum wage).
Raising minimum wage destroys opportunity for people who haven't had a job before to learn workplace skills which would allow them to go get hired at a better job later on. If that job's no longer there (see above), you can't learn those workplace skills and won't be able to get a more advanced job. That sure helped you, didn't it? Curiously enough, somehow, same crowd doesn't see people who do internships for free or volunteer as something that must be prohibited as evil exploitation.