That is a complicated issue.
In general, there are two answers to the question you pose, with many shades in between.
First, some people question whether Vatican 2, or the various acts that followed it, with or without various approval, had the authority to change the things that were changed. This could be rephrased, “Is the new order of the mass lawful?”
Into this camp, fall the various sedevacanists, certain Orthodox commentators, and to an extent, people (including perhaps two popes) who desire to “reform the reform,”
although they usually stress the second theme (see below).
The second common criticism asserts that the new order of mass led to apostasy, indifferentism, blasphemy and confusion about the nature of the sacrament. Though the breadth of criticisms could fill a book, it comes down to asking “was the replacement of the tridentine mass with the n.o. prudent?”
Into this camp, fall SSPX, traditionalists who attend their diocesan parishes, those who advocate for “the reform of the reform.”
Like I said, there is considerable movement between these two broad camps, and one frequently uses the arguments of the other. Hopefully, though, that sketch provides a fair description why some people take an “anti ordinary form” stance, which may help in analysing any given critique.