The horizon problem is the problem of determining why the Universe appears statistically homogeneous and isotropic in accordance with the cosmological principle. For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate.
The argument is that the early universe could not have had time to evolve to thermal equilibrium without an inflationary period. But why we are assuming that the early universe needed to evolve into this state in the first place? Why couldn't it have formed already in thermal equilibrium? The quoted argument seems to make unnecessary assumptions. To suggest that the universe needed time to equilibrate is to suggest that it was once - sometime prior to recombination - not in a state of thermal equilibrium, correct? But why would we make such an assumption?
I have had a look at this Why does the homogeneity of the universe require inflation? question and the accepted answer claims:
Creating a universe where the temperatures were random in different parts of space and had an opportunity to come in thermal equilibrium before going out of causal contact (as a result of inflation) is more natural
But I don't agree that this is more 'natural'. To me this logic is totally backwards. A universe with a random temperature distribution is much harder to explain than a uniform one. If you're going to suggest that the early universe contained random energy fluctuations, surely you have to explain why that would be the case? If the entire universe somehow came into being in one great Big Bang, then surely it makes significantly more sense that it would be the same temperature and composition at every point in space? Only developing anisotropies afterwards (probably due to quantum fluctuations).