What exactly is critical listening? Who does it?

Critical listening is necessary if one is to progress, also necessary to have a knowledge base/listening encyclopedia in order to obtain a reference or references as a goal. I spent far larger percentage of listening time in critical listening mode to my systems and others in early years, decades. Over time as I've come closer to my goals, far less time spent in this mode, mostly I admire the sound if I do go into this mode. 

Critical listening mode shouldn't always be seen in a negative light, it is a necessary tool in the audiophile tool bag.

Critical listening means optimizing the setup and listening closely to what the system is doing. 

The MORE effective critical listening must happen in more understanding of audio sounds because our ears trick us. All audio systems (incl. million $ systems) sound/behave veiled & distorted like speakers below. 

Listen to spkr sounds. Not Jay’s voice.

Your audio system sounds like the left speaker

Alex/Wavetouch audio

Maybe it’s like going to a museum and looking at a painting done by a master. For many just visually looking at it, it achieves lots of enjoyment. And then for others, they understand all the work related to color choices, brushing techniques, contrasting, depth perception - they put a lot of thought in looking at the Picture because they understand what it’s all about.  Most mere mortals have no clue.

Many of us mere mortals may wish we better understood all that goes into the picture which no doubt would allow a better appreciation for all it took to achieve it.

There are some remarkable paintings in this world and I wish I would’ve taken some art classes in college. 

There are different types of "critical listening" for different purposes. In audiophile land, I think it is often meant to describe listening for shortcomings in the presentation of a system or given component. But it can also involve listening to compare different pressings of the same record, to evaluate their respective merits. In musicology, there are also different types of critical listening- one might be to analyze motifs or how it fits into the overall body of that composer's work, its influences, historical context, etc. Forensic musicology often involves picking out allegedly infringing phrases or elements and finding historical precedent for their common usage as building blocks by other authors. I think you need to provide context to afford more meaning to the term. To me, I most often associate it in home audio reproduction with listening to where a system or component reveals its shortcomings. 

Correct.  Get busy now and let us know your findings. Chop chop!  Enjoyment is right out! 😉

Myself:  guilty as charged.  Call me Mr. Critical.  Just be nice about it.  Not too critical, please.