There are many strange coincidences in our world. The mass of the electron is 2000 times smaller than the mass of the proton. Why? The only known reason is that if it would change few times, life as we know it would be impossible. The masses of the proton and neutron almost coincide. Why? If one of their masses would change just a little, life as we know it would be impossible. The energy of empty space in our part of the universe is not zero, but a tiny number, more than a hundred orders of magnitude below the naive theoretical expectations. Why? The only known explanation is that we would be unable to live in the world with a much larger energy of vacuum.
The relation between our properties and the properties of the world is called the anthropic principle. But if the universe were given to us in one copy, this relation would not help. We would need to speculate about the divine cause making the universe custom built for humans. Meanwhile, in the multiverse consisting of many different parts with different properties, the correlation between our properties and the properties of the part of the world where we can live makes perfect sense.
Can we return back to the old picture of a single universe? Possibly, but in order to do it, three conditions should be met: One should invent a better cosmological theory, one should invent a better theory of fundamental interactions, and one should propose an alternative explanation for the miraculous coincidences which we just discussed.