The simple answer is that it is correct. But the real question isn't about English grammar, but about the differences between Italian and English grammar, to see why we would express things differently.
I can see two reasons you might not be able to say this or why if you did, it might not have the required meaning.
Firstly, reflexive verbs are much more common in Italian than in English. They are explained here. In addition there is no exact equivalent of "myself", so they would just say mi lavo "I wash me" where we would say "I wash myself" or, more usually, use the verb intransitively: "I wash". Because they are so common, usually corresponding to intransitive verbs in English, or sometimes to a passive construction (mi chiamo "I am called"), you would miss the sense you get in English of emphasising the use of transitive verb, and that you are both the subject and the object. Rather, they are usually used for things you normally do by yourself (mi rado "I shave") without actually thinking about doing something to yourself.
You will have noticed I have not used the verb "to teach". This is because of the second problem:
In English, teach can take two objects:
I teach children chess
and although one of these is considered an indirect object as shown by the fact that we can say
I teach chess to the children
we usually just allow the two objects with no preposition. You can't do this in Italian. You always teach the subject a "to" the people, as shown in Collins Italian Dictionary
to teach sb sth or teach sth to sb insegnare qc a qn
This means that you simply cannot teach yourself, unless you are the subject being taught.
Thus we see that it is quite reasonable to have to express the same thing in different ways in different languages.