Why did Walt have to teach high school chemistry?

To my knowledge the series never really touches on this. The link that @Walt provided above is informative but I don't think there is much more specific information to be had.

One of the great things about Breaking Bad are all of the back stories of the characters that we can only speculate on. This is why Better Call Saul is so compelling.

To answer the question specifically I can only offer what I believe good writers know how to do. Good writers know how to write empathetic not sympathetic characters.

To make the show work the viewer must see some of themselves or someone very close to them that would 'initially' make the same decisions as Walter White. Part of that empathy is questioning your own decision making in the course of your life and as we all often do, regret certain decisions that we see in retrospect, as crossroad decisions. "If I only ....".

Who amongst us hasn't harkened back to high school glory, college freedom, or early life successes? How about the white hot stardom of child actors, one hit wonders, or wall street 'geniuses'?

Walter White had massive success very early in his life and as is the case with many people who achieve early success and hit a roadblock, he did not handle it very well. Simply, Walter White did what most of us do and that's settle. Success one time is VERY hard and Walter was basically there. Success a second time can seem impossible and eventually human nature takes over.

Walter White HAD to teach high school chemistry because he settled and if it were not for the awful car wash boss and humiliating experience of washing his own students car, there might have never been a show.

Walt's life has been a failure in many ways. Although his (extended) family is a good family (people are flawed but not malevolent), he had so much potential compared to where he ended up.

This is the foundation of the show's plot. Walt starts the meth empire not only for the money (that's just the justification he uses), but also because he wants to prove to himself and the world that he is a force to be reckoned with.

This means that before he starts the meth empire, he must therefore be leading a pathetic life where his potential is wasted. His job as a teacher tries to illustrate that point.

But is it ever explained why he is teaching chemistry in a high school?

Teaching is often considered to be a "lesser" job compared to practicing.

Your question already implies that you are aware of this: why is Walt merely teaching chemistry, and not practicing chemistry professionally?

So the most direct answer to your question would be because the plot needed the story to start off with Walt suddenly realizing that he is leading a pathetic life. The teaching job illustrates the sad life he is leading.

Please note that the teaching was not the sole indication of Walt's pathetic life (as he saw it).

• In the opening scene (breakfast at home), it is made clear that the water heater is broken, and that it has been the case for a long time. Walt is clearly not doing well financially.
• In somewhat of an ironic twist, Walt is also a bad teacher. Not because he is incompetent, but because he is overqualified to the point of forgetting to explain things that are obvious to him but not the students. This presents itself as Walt often having backtrack on his statements to clarify, which makes it seems as if he doesn't know what he's talking about (to a layman). From the pilot: "Chemistry is the study of what? Chemicals! No! Chemistry is... Well, technically, chemistry is the study of matter. But I prefer to see it as the study of change." Walt can't even agree on a description for his own field. Is it the study of chemicals, matter, or change? He tries to make distinctions that his students cannot comprehend. (Later in the show, we see Walt making the same mistake with Jesse. He explains things as he understands them, not how Jesse understands them).
• Walt has to work two jobs and is working himself to death for a family life where he isn't even allowed to have a plate of non-vegan bacon.
• Walt doesn't even get the minor authority over his own students, as he has to suffer the humiliation of cleaning their cars in his second job.
• The world shits on Walt. Skyler babies him and Hank considers Walt less manly than him (Hank is not malevolent about it and doesn't even mean to, but he does override Walt in terms of masculinity). I also seem to remember an early scene where Skyler suggested Walt asks Hank for help with what should have been an easy household chore. This makes Walt feel emasculated by his own wife.
• In general, the world sees Walt as the disappointment he grew up to be, rather than the genius he actually is. This very much drives Walt's need to show the world that he is better than they think of him.
• Out of universe, the car that Walt drives is considered well built, but it never sold well, for no reason other than it never being popular. Similar to Walt, it had potential but ended up as being a failure to start.

If you want to dig deeper into the question, as to how his life became so devoid of potential, that is mostly a matter of bad luck.

Walt did not do anything specific to deserve it. He made some bad decisions (e.g. leaving Grey Matter), but it is important to note that this decision can only be called bad in hindsight. At the time, Walt could not have known that Grey Matter would become a highly succesful company.

He didn't even leave Grey Matter for professional reasons. It has to do with Gretchen on a romantic level.

But the most important part is that his decision, while essential to his lack of financial success in the future, was not a bad decision at the time he made the decision.
For all he knew at the time, he could have stayed with Grey Matter, which would have remained to be a failing business, and missed out on some golden opportunities because he was too loyal to his failing business.

Walt zigged, when he should've zagged (just like the rest of the world). The fact that it was outside of Walt's control only contributes to how much it annoys him to be a failure, and how he feels the world has wronged him.

Great question. I wondered this myself. Actually, being a College Professor at UNM might give Walt White more time at home or with Walter Jr. Teaching High School is rather demanding hours. Teaching at University of New Mexico -- he could choose what classes he would teach each semester. Some Professors only teach 2 or 3 classes each semester. Plus, college classes typically are taught twice or three times per week instead of 5 times a week at High School. Plus, they can teach one class at night and another class at night every other day. I think Walt White should have done this. Maybe he didn't want to do the research portion because of how his first research endeavor with Gray Matter ended so dramatically. But Walt could do all kinds of research at a University. For a genius like him. He should've just done further "Crystallography" research.

Plus, he'd have less papers to grade. He could even teach graduate classes which typically have much smaller number of students.

BTW, didn't the original Pilot episode show Walt White washing students' cars' wheels? And the two students were kind of laughing at him. Why did they change that? That further showed the humiliation Walt experienced which helped motivate Walt to make an extreme change. Maybe it was an "end credits" payment issue and they later edited those two students out. Weak. Just like why would you want to do an "advertising job" flipping a sign? Motivates some people to elect a life of crime instead of working jobs like that. I would never choose crime ever, no matter what. But I know what it's like to work nothing jobs or be at the bottom of the barrel and considering suicide.

Walters motivation to do things in his life were mostly based around his family. Seemed like a son with Cerebral Palsy and Skyler's constant involvement in his decision making process reinforced the concept and well being of 'Family' on top of anything else.

Taking care of a mentally challenged kid requires lot of strength and support network as I have witnessed in my own family. May be this is the reason Skyler chose to be in the same city as her sister and Walter getting whatever decent job he could to support his son by giving time and energy which lot of researchers/academics lack now a days with constant pressure of sustaining the research grant/research job, i.e less stress on job and more attention to the family.

He sacrificed his career to be with family(very big though), this seemed to cloud his judgement of right or wrong in the whole series i.e do whatever it takes to provide for family.