This critique (and it is the by far the most common critique of MMT I've heard) boils down to this:
"MMT may very well be an accurate depiction of reality, but the problem is that if people start to see it as an accurate depiction of reality then inflation might go up."
That's definitely a problem for a certain class of people (creditors and investors).
MMT is controversial because, if true, it's undermining a lie that is supporting those interests ("keeping inflation as low as possible") over the interests of society as a whole.
"MMT may very well be an accurate depiction of reality, but the problem is that if people start to see it as an accurate depiction of reality then inflation might go up."
That's definitely a problem for a certain class of people (creditors and investors).
MMT is controversial because, if true, it's undermining a lie that is supporting those interests ("keeping inflation as low as possible") over the interests of society as a whole.