James Webb Telescope Confirms That the Universe Is Expanding at Different Speeds

We don’t really know - you are right to ask this question. There are two methods and they disagree with each other. JWST is precise enough to rule out a simple reason like instrument imprecision.

So remaining possibilities are new physics, a deep flaw in our assumptions/methods, or a universe which is not uniform (but in a peculiar way).

I don't want to discourage question-asking but you're now asking someone to give you a background on a physics phenomena without them knowing your starting level. It's awesome that the poster you're replying to introduced a new concept to us (not something I was thinking about, either) and literally taking the thing you quoted: "time does not flow the same everywhere" into Google will give you a starting point for your quest - you'll see even from the blurbs on the search result page that per relativity, time changes depending on where and how fast you're traveling. You can then dive into what that means you want to as well.

I good followup could be something like "I read about relativity and I still don't understand the connection you're making to this current article or something like that - but it doesn't seem fair to skip a basic Google search before asking for elaboration.

Cosmology feels a lot like quackery these days.

Does it even bother to rely on physics? Physical experiments show explosions do not propel all matter at the same rate.

James Webb telescope recently found galaxies that were “too old”, would have formed right after the Big Bang. The prevailing wisdom was all matter spread out evenly due to the Big Bang, then coalesced into galaxies (I emailed various researchers to confirm I understood this was indeed the consensus).

But again, other physics shows that clusters of matter ejected from explosions are never uniformly distributed.

Just more evidence the well educated (I assume if it’s concensus driven even the best educated agree) are just typical people and their expertise should be challenged constantly rather than sit back and assume things are figured out.

As Asimov illustrated in the Foundation, if you aren’t measuring for yourself you’re serving someone else’s interpretation.

Hyper-normalized social society just leads to normalization of outputs, which helps preserve and propagate poor science.

This is a poorly written article, it almost appears whole paragraphs are missing. For instance the phrase "an impossibly high value when compared to Planck’s measurements" is not explained at all. (Planck was a physicist, but I suspect they're referring to https://en.wikipedia.org/wiki/Planck_(spacecraft)

I think what it's actually saying is that we've confirmed that the Hubble tension is real. Whether or not that means different parts of the universe are accelerating at different speeds is still not clear. If the meaning of the results is deeper than that, it seems to have completely eluded the author who nonetheless wrote a breathless exaggeration of the findings.

EDIT: In 2024 actually I have to wonder if any humans were involved in the making of this article. It certainly doesn't appear to have passed an editor's eyes.