Art is often seen as a reflection of life, for good or for bad. Thus, it is not surprising that much of art contains elements that may be considered, well, downright depressing and full of conflict that grabs the attention. Everyone agrees that artistic creators should have access to the wide range of human emotions in the characters and events depicted within their works, and no one blames them for attempting to inspire the same range within their audience. Indeed, one of the things most disquieting about Plato's The Republic is how Socrates bans any emotional art from his supposed utopia. Without the influence of the tragic, we would not be able to experience some of the most critically-lauded works that have ever been created.
However, art is also seen as Escapism, and rightfully so. Everyone agrees that people have their own tastes in the media they consume, and have their own particular limits in how much fictional sadness and "interesting" conflict they are willing to put up with, simply because how everyone has their own real life problems to consider. It is not too much to ask for entertainment to be, you know, entertaining. If someone prefers a Warm and Fuzzy Feeling over how the realism and catharsis of a tragedy or Current Events-based dystopian literature allegedly gets you to "think" (or enjoys either one depending on their mood), then more power to them. Only a very few want a world where everyone believes that "Silly Rabbit, Idealism Is for Kids!" and that the only True Art Is Angsty, and anyone who thinks happy art cannot be good art is certainly not understanding enough. Angst aversion, then, is the situation occurring when these two conceptions collide: The personal tendency for a person to avoid a work once they hear it has a Downer Ending, or is generally filled with sympathetic characters that will be put through hell for nothing.
This should not be confused with Darkness-Induced Audience Apathy, though both can be caused by the same general issue. Also not to be confused with Angst? What Angst? which is when a character exhibits no or little angst in response to what should be a traumatic event.