Why is wave-function collapse still being taught in quantum mechanics? I don't really understand why wave-function collapse is still being taught while we seem to have better interpretations of QM available nowadays.
During the early development of quantum mechanics the measurement problem was a heavily debated topic, resulting in a general acceptance of the so-called Copenhagen interpretation. The two main problems with it are


*

*It is not clear what physically defines an observation.

*There is a certain faster than light interaction, thought this does not include faster than light travel of information.


Furthermore, the idea that the universe is nondeterministic was not appealing to some, for example to Einstein.
Since 1957 we have the "Many-worlds" interpretation of QM which resolves both these problems, makes QM deterministic again and gives a (IMO) much more physical interpretation. The original name Hugh Everett gave to his theory is "Correlation Interpretation" which I find actually more clear. Perhaps "Observer Entanglement" would be even more natural in the current idiom.
This theory was first mostly ignored, and even now seems to still not get the attention it deserves. Why are teachers often still teaching wave-function collapse, with all its shortcomings, when they teach QM?
 A: When something is taught a certain way in textbooks, then two things need to happen for that to change:


*

*Leading professionals in the field have to agree that the new approach is better, and start using it nearly universally in their research papers.

*The new approach gradually filters down into graduate textbooks, then upper-division undergrad textbooks, freshman texts, and popular writing.
An example of this process is the replacement of relativistic mass with invariant mass, which is still ongoing after several decades.
In the case of MWI versus Copenhagen, step #1 hasn't happened yet and probably never will. In nearly all applications, the choice of one or the other makes zero difference, even aesthetically. MWI also comes in a variety of flavors; some people do talk about measurements and splitting of worlds, while others find those concepts wrong or unhelpful. My own view (which has evolved as I've learned more about the subject) is that MWI is aesthetically preferable, but that if we want to explain why measurement seems to work in the way it does, ultimately we should probably talk about things like decoherence, and then the way measurements seem to work emerges as an approximation. (And the approximation can be bad if the measuring device is mesoscopic.) Personally, I use the language of MWI in talking to my students about QM, but I don't think it's wrong to use Copenhagen. Most freshman texts don't even talk about these issues, e.g., collapse is never even mentioned.
I do find it objectionable when upper-division texts introduce Copenhagen as if it were the only way to look at things, and without explicitly naming it as the Copenhagen interpretation.
A: *

*There are many interpretations, and while there are good arguments in favor of one or another, they are currently not distinguished experimentally. Therefore it is often considered prudent to leave the question of which interpretation is best to the field of philosophy, and focus in a physics course on the falsifiable aspects of the theory. The field of quantum interpretations is too deep to do the subject justice in an ordinary quantum mechanics course.

*The "Copenhagen Interpretation" is not very well-defined, but given point #1, it has several advantages over the others. One is historical inertia, but more importantly is its minimalism and instrumentalism. In its "textbook version," it avoids taking a position on the philosophical aspects of the theory, and focuses on calculation. It is often associated with the "Shut up and calculate!" mantra. "Collapse" of the wavefunction is not taken too literally as a dynamical process, but merely as a calculational tool. Quantum textbooks/courses tend not to dwell on the philosophy of Bohr or Heisenberg, and rather leave interpretation open to student preference should they pursue it through other resources.

*The philosophical problems with the interpretation, such as describing the experimental apparatus or observer quantum mechanically, are currently not an issue for experimentalists testing the predictions of quantum mechanics, though in response to some comments perhaps I should add that some interpretations tend to be preferred by different subfields of physics, for example unitary wave function evolution is more useful for cosmology, a case where there are no observers external to the wave function of the universe to cause it to collapse. Something similar might be said for quantum computation, where something like an AI could potentially be put in superposition.
A: So we are taught collapse at school, although there is no experimental evidence of collapse. You don't think this is good.
You suggest that we are taught many-worlds instead, although there is no experimental evidence of many worlds. Why is it better?
I would say there is no generally accepted interpretation of quantum theory (the mere existence of numerous interpretations seems to be an evidence of that). So which interpretation should be taught at school? I don't know. But do we need to change an unsatisfactory interpretation by another unsatisfactory interpretation?
You may believe that many-worlds is a satisfactory interpretation. According to some surveys, the majority of physicists do not favor many-worlds. So it is not obvious that students should be taught many-worlds. Should they be taught collapse? I don't think so, not without caveats.
A short answer to your question would be "because education has a lot of inertia", and it is not obvious that this is a bad thing.  
