Thanks, I'm glad you found it useful.

Let me start with a rather mathematical definition: Unitary operators[1] are invertible operators that preserve the inner product of the Hilbert space they live on. They are used in quantum mechanics to describe the evolution of the state of a physical system. The preservation of the inner product in this context (roughly) translates to the statement that probabilities of measurement outcomes don't change, i.e. that probability is conserved. Invertibility, in turn, means that even though we can only talk about probabilities in quantum mechanics, we do so in a deterministic way. Put differently, if you know the state (= the wave function = the set of probabilities) of a system at a time t1, the state at other times t0 < t1 or t2 > t1 is uniquely determined. That is, using the unitary evolution operator, you can basically go back and forth in time, thus determine what the state of the system will be in the future or what it was in the past. In this sense, quantum mechanics is still a deterministic theory, even though we can't predict measurement outcomes with 100% certainty anymore. (Namely, what we can do is deterministically predict probabilities.)

Now, the problem with the collapse of the wave function (or the measurement process in general) is that it breaks this, i.e. the collapse is non-unitary. Probabilities are changed and the process is neither reversible nor predictable, i.e. entirely non-deterministic. If you have a system in a superposition of states A and B (say with a chance of 50% of measuring A or B, respectively) and you then measure A, then – due to the collapse of the wave function – the state of the system will be A with a probability of 100% directly afterwards. The probability changes and you have no way of knowing anymore what the state was before the measurement. (Nor did you have any idea that you would measure A and not B before actually carrying out the measurement.)

On the one hand, this shouldn't come as a surprise because the fact that "god plays dice", i.e. that systems might be in superpositions of states until they are observed and have to decide, is at the heart of our interpretation of quantum mechanics. On the other hand, this is weird because all the equations governing quantum mechanics are unitary evolution equations, so actually shouldn't allow non-unitarity. The crucial point seems to be that we still haven't nailed down what a measurement actually is and that we use classical terminology to describe it (i.e. we distinguish between the quantum systems and our classical measurement devices). But if our world is entirely quantum, then our instruments should be quantum, too, in particular they should not be able to bring about a non-unitary time evolution. Hence, the question is how the unitary interaction of a small quantum system and a large quantum system (like a measurement device) can lead to an apparent break of unitarity – even though it is actually not. A related question is how classical behavior emerges from quantum behavior for large objects (that is, why is our world entirely classical when the microscopic world actually is not).

Concluding, my reference to the non-unitarity of the collapse of the wave function served to remind the reader that the collapse is not compatible with unitary time evolution and thus explain why, as a concept, it likely (hopefully) won't survive the next revolution in physics.

Let me know if that helped!

[1] https://en.m.wikipedia.org/wiki/Unitary_operator