If this were actually a cause of problems in American education, I might consider it, but it isn't. The problem with American education is, first and foremost, crumbling infrastructure and lack of social support and welfare. You cannot teach children whose lives are made unstable by deteriorating neighborhoods, parents who lack adequate work, inadequate access to mental and physical health care, etc. Until that is fixed, nothing else can be.
But this is far afield. The teachers union can in no way be shown to be the cause of any problems in American education, although I will agree that education is not the prototypical place in which unions should be strong, because there are countervailing interests that are not present in regular employment. Schools exist primarily to serve children, not to produce and sell commodities. Schools, of course, are not corporations, and so that you choose this example is not surprising.
Corporations do not serve the interests of their employees, which is what you posited by raising a false dichotomy between white collar (e.g., an engineer) and blue collar (e.g., factory or construction) workers. Both white collar and blue collar workers--with the exception of corporate executives--are in the same boat. Corporations, by law, must serve the interests of their shareholders to the exclusion of everything else. That includes their white collar and blue collar workers, whose interests in high pay is diametrically opposed to the corporations interest in high profit.
Corporations only "create jobs" by fiat of the economic structure, not because they have some magical "job creating" substance in them. And this is irrelevant to the point, which is that corporations serve the interests exclusively of investors (the capitalist class) whereas unions serve the interests of working people. The former (the investing class) is a tiny class of multi-millionaires and billionaires whose interests as investors is, as I have explained, directly opposite those of working people (higher wages mean lower profits and vice-versa). This should explain why you should not be surprised that any rational person not a member of the investing class would side with unions over corporations.
Let me guess, a business class? No offense, and I don't mean to be harsh (honestly, you seem like a nice enough gent), but you are the future problem of this country and represent the mindset that must be broken if the nation isn't to continue to degrade.