I think an antonym or the opposite of "teach" is "indoctrinate".

I'm thinking of the negative connotation of this word. One dictionary definition of indoctrinate is:

          To imbue with a partisan or ideological point of view

In essence, there is no teaching here, in the sense that teacher and student bounce ideas, concepts, opinions, and such off of each other. Indoctrination often dispenses with "give and take" between teacher and student. It is often someone trying to cram their beliefs down the throat of the recipient.

Great teaching allows for discussion, questioning, opposite viewpoints, and more. With this type of teaching, quality learning takes place.

I like the idea of brainwash or may be condition. It is not the same thing to teach someone as just to make students regurgitate back what the teacher has said to them. 

Propagandize - what Hitler or Stalin did in Germany and Russia respectively (and in other countries that education is toyed with by government) is very different than teaching people. It is just delivering one-sided, subjective information as fact. 

I think I am thinking of this more philosophically as literally though. 

I consulted a handful of online thesauruses, and the only antonym listed was "learn." Interestingly, "brainwash" was used as an example of a synonym. I don't really see where learning is an antonym, though. As teachers, most of us have a bit more nuanced and perhaps expanded definition of what "teaching" means.

Most opposites are stark in contrast (think black and white/ night and day). Given that teach means to train or educate, nothing really exists as a contrast to the term. The outcome of teaching is learning (for me, this is not an opposite). I would suggest that no true opposite of teach exists (unless you count "not teaching").

The opposite of teach could be ignore.  Teaching is about giving knowledge and/or information.  We learn from those who are not necessarily intentionally teaching us as well as those who set out to give us knowledge.  A parent might take the opportunity to teach a toddler manners or we might learn simply by watching a parent.  Someone who ignores others and does not set an example is intentionally not teaching and leading. 

I would have to say the closest opposite of teach is to learn.  Absorb could be another close relative of learn, because when you're learning something, you're absorbing it.  And here's another one:  when you teach you educate.  So, someone who is receiving the teaching is educated.  To teach is to also impart knowledge so a person who is taught is knowledgeable.  I hope these definitions help.  Good luck!

We might argue that the opposite of teaching is brainwashing. Teaching is supposed to offer thinking skills that enable a person to perform tasks, organize ideas, and come to conclusions on his/her own.

Brainwashing seeks to do the opposite. Brainwashing (indoctrination) seeks to pre-organize ideas and to present conclusions, not build skills that enable a person to generate them originally. 

The only one that I can come up with is "learn."  It's not quite the opposite of teach because the true opposite of teach would be some word that means to take knowledge away from someone.  But "learn" is probably your best answer here.