Why does a push_back on an std::list change a reverse iterator initialized with rbegin?

The standard says that iterators and references remain valid during an insert. It doesn't say anything about reverse iterators. :-)

The reverse_iterator returned by rbegin() internally holds the value of end(). After a push_back() this value will obviously not be the same as it was before. I don't think the standard says what it should be. Obvious alternatives include the previous last element of the list, or that it stays at the end if that is a fixed value (like a sentinel node).

Technical details: The value returned by rend() cannot point before begin(), because that is not valid. So it was decided that rend() should contain the value of begin() and all other reverse iterators be shifted one position further. The operator* compensates for this and accesses the correct element anyway.

First paragraph of 24.5.1 Reverse iterators says:

Class template reverse_iterator is an iterator adaptor that iterates from the end of the sequence defined by its underlying iterator to the beginning of that sequence. The fundamental relation between a reverse iterator and its corresponding iterator i is established by the identity:
&*(reverse_iterator(i)) == &*(i - 1).

I think to understand this, it's best to start by re-casting the for loop as a while loop:

typedef std::list<std::string> container;

container testList;
testList.push_back("a");
testList.push_back("b");
testList.push_back("c");

container::reverse_iterator itList = testList.rbegin(); 
while (itList != testList.rend()) {
    testList.push_back(*itList);
     ++itList;
}

Along with that, we have to understand how a reverse_iterator works in general. Specifically a reverse_iterator really points to the element after the one you get when you dereference it. end() yields an iterator to just after the end of the container -- but for things like arrays, there's no defined way to point to just before the beginning of a container. What C++ does instead is have the iterator start from just after the end, and progress to the beginning, but when you dereference it, you get the element just before where it actually points.

That means your code actually works like this:

After that, you get pretty much what you expect, pushing back B and then A, so you end up with ABCCCBA.