What is so problematic in the information paradox? I'm not sure I see the difficulty in the black hole information paradox. The outgoing Hawking radiation is not causally connected with the information in the particles inside. If the hole has evaporated you can't tell what was inside by looking at the Hawking photons. Strominger said that black holes are the cause of the breakdown of the physical laws in our universe. He and two others made a huge calculation to solve the paradox and rescue the physical laws. They assumed soft hair for a BH. Like this, no information is lost. Firewalls are not needed anymore (these were proposed to deal with the problem of entanglement monogamy). About 5000 math terms were needed to arrive at the a priori known value of 12J, the angular momentum of the hole. Rather incredibly they arrived exactly at 12.
But anyhow, why is it so hard to assume that information is lost? If you can't trace matter back to matter that is not there anymore, so what? If the (outgoing) Hawking photons can't be causally connected with the stuff inside the hole, so what? Particles inside disappear and particles appear on the outside. As simple as that. Is unitarity lost? Isn't that also in the case of a wave function collapse? Or when a particle pair is created? The created particles have no causal relation with what came before.
So why inventing strange kinds of entanglements of the Hawking photons with the interior of the hole? Why is the disappearance of particles constituting the BH and an independently appearing of Hawking radiation problematic?
 A: With Hawking radiation being thermal (carries no information), black hole evaporation is fundamentally irreversible. This is incompatible with quantum theory, as @Andrew says. So, the problem is to find out what happens with the information.
Solution Attempts Summary:

*

*Denial: Nothing falls in/black holes don’t form. Nope. Just wrong. Note, this kind of solution isn't Hawking being misquoted, or whether they form being not well defined.

*Anger: The observer burns up in a giant firewall. Not Even Wrong.

*Bargaining: Information comes out. Presently the most popular solution, as it is supported by the gauge/gravity duality.

*Depression: Remnants/information stays in. Unpopular because nothing can be calculated.

*Acceptance:  Non-unitarity. Not ruled out, but even more unpopular than remnants.

Reference:  Sabine Hossenfelder
A: Quantum mechanical evolution via the Schrodinger equation (or whatever your favorite formalism is) is unitary. We can start with a pure state with some particles and no black holes, and throw these particles at each other to form a black hole. We then wait for the black hole to evaporate. Eventually it evaporates completely and, according to Hawking, we get radiation that is thermal. This means the state is a mixed state. There is no unitary transformation that takes us from a pure state to a mixed state, so quantum mechanical unitary evolution has apparently broken down [Note: if you don't know about mixed states, the key takeaway is that unitary evolution is not possible of taking us from the initial state to the final state]. This is a contradiction if we assume that the whole system can be described quantum mechanically.
A solution to the problem needs to explain exactly goes wrong. For many (including me), preserving unitarity and quantum mechanics is paramount, which suggests there must be a problem with Hawking's calculation and that the radiation is not really exactly thermal (if only we could calculate its state). If you want to solve the paradox by saying that there is some measurement that happens breaking unitarity, you have to explain exactly where and why the measurement occurs, and how this measurement produces a thermal spectrum. You're perfectly free to wave your hands and think about things you find more interesting, but you won't make a contribution appreciated by people who take the problem seriously without a detailed derivation showing how your mechanism reproduces Hawking's calculation.
