Rothko's paintings are ideas just like Duchamp, Kandinsky, Richter and Pollock.
There are two kinds of people that criticize them:
- First kind, the ones that criticize and challenge their ideas. Not the process, not the method, not the work itself. Examples - David Sylvester and Michael Peppiatt who criticized Francis Bacon [0]. Those were constructive, extremely interesting encounters that challenge artist's notions and provide different perspectives. They vehemently opposed the artist [1], but thoughtfully to incite and open new conversations around their ideas. They also understand the historical time frame and overall art history, especially the turn of the 20th century.
- The second kind, criticize materialistic, physical and methodical manifestations of art. Such as trying to judge how relatively easy/hard was it to paint; "Any one can do that"; paintings are trash because I personally do not resonate with it visually; no revolutionary methods or interesting ways of physically making the art, etc. They also try to find deeper meaning where there isn't and make up far fetched meanings to justify their understanding of something that is not meant to be literally understood. There are also people on the other end of the spectrum such as people working in the galleries that try to bullshit you with their sales pitch which often contains non-sense and wordplay.
The second kind do not understand art.
[0]https://www.youtube.com/watch?v=xoFMH_D6xLk
[1]https://mitpress.mit.edu/sites/default/files/titles/content/...