Yes! Let's move on. What is exactly wrong with the inflation theory?
IMO, everything! It's dead. It's 'made up'. It's mythical. It's metaphysical. It's impossible to empirically demonstrate now and forever. It's faith, not science, and I know the individual that came up with it. Besides the obvious physical warts, nothing much. Other than that, it's mathematically rather attractive.
I get that testing in a lab has proven elusive so far, but, as has been brought up so many times already, so have most things in theoretical physics at one time or another.
The difference is that most theoretical physics (even exotic dark matter theories) have some hope of empirical vindication, if not now, somewhere in time by someone. Inflation however is dead. It's non existent. It has no effect on anything anymore according to standard theory. It's no better IMO than a mythical dead deistic religion in terms of empirical physics in the preset moment. Worse yet, Guth can not ever even hope to empirically validate inflation and thumb his nose at me, not even if we both live to be a billion years old.
So, I don't think that's grounds to dismiss it entirely.
From my skeptical view, there's no reason to consider it anymore than I would consider any other dead deistic "god did it' "explanation".
What is the *theoretical* argument against inflation theory?
Inflation is a figment of a single individual's imagination and become a popular "meme" in a subset of human scientists.
Where does it breakdown or seem questionable?
At the level of empirical physics. It will always and forever remain "unseen" to any and all human beings.
Isn't it something already measured in the universe?
No. Photons are measured. One might say homogeneity is also "measured". Guth developed (postdicted) inflation to match those measurements and it is a highly "subjective interpretation" of those measurements. There is a subtle but important difference.
(As a layman, I also get that distant measurements seem fantastic. For example, I've often wondered if the red shift indicating acceleration wasn't also caused by gravitational effects from space debris or just the effect of such a long distance; something else other than acceleration.
But mainstream will crucify you for "doubting" them on this or any other "interpretation" of those same observations.

They will insist you interpret a whole host of subjective assumptions about those measurements their way too sooner or later.
But since I'm not formally trained in this subject, I'm pretty sure that has either been considered before or is just not relevant. That is, I think it is highly unlikely I'm going to out-think the great thinkers based on so little knowledge.

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It's only irrelevant if you *assume* we as a species already have almost everything about the universe all figured out. That's silly IMO. Redshift could be related to something other than expansion, but expansion is a valid empirical "interpretation" of that data. It's not expansion I have trouble with, it's the claim about the "causes" of that expansion I have a beef with.
I do however try to stay open minded about the fact that other 'interpretations' of redshift "could be" just a valid, but I personally do favor an expanding universe over a static one just like the mainstream.