How does inflation justify the nonexistence of magnetic monopoles? It is said that inflation justifies that magnetic monopoles don't exist. Can anyone explain how inflation theory explains the non existence of magnetic monopoles?
Let me start off by stating that scientists have not conclusively proven that magnetic monopoles do or do not exist. There has never had a confirmed detection of one so the jury is still out on if a magnetic monopole can or does exist at all. That being said, if monopoles do exist, no one has a good explanation for why we haven't detected one yet. There are hypotheses, but no solid proof.

To get to your question now, I think it is an incorrect statement to say that inflation theory explains the non-existence of magnetic monopoles. What inflation theory does potentially explain, is the extremely low density of magnetic monopoles in the universe. The idea here is that magnetic monopoles, for some unknown reason, are extremely unlikely to form, even in the intensely energetic and hot crucible of the Big Bang. Some estimates say that for 1 magnetic monopole that formed, $10^{29}$ "normal" particles formed, making magnetic monopoles extremely sparse and rare.

Where inflation theory comes in is that it says the universe expanded exponentially fast. If the monopoles were already sparse before this extreme expansion, the expansion would have only served to cause the magnetic monopole density in the universe be practically zero. It is quite possible that, post-inflation, the magnetic monopole density in the universe is so low that only one exists within the observable universe. Good luck finding that single particle out of the $10^{80}$ particle haystack.

In my mind though, that doesn't really answer the question as to why we don't see magnetic monopoles. Inflation just makes them extremely sparse, but why did so few form to begin with (assuming they formed at all). As I said above, nobody knows. A potential answer (without any evidence) is that magnetic monopoles are extremely energetic particles (e.g., with energies greater than the LHC of 14 TeV). If they have such extreme energies, even the Big Bang wouldn't have formed many of them. But again, that's just a guess.

Only time will tell what the real answer is.