Because we have no control over it and there is no clear alternative that is obviously superior. Arch isn't a lock to be a better QB going into the SEC championship and playoffs and Owens definitely isn't.
One of my sad Aggie friends was lamenting the upcoming loss of Connor Weigman and saying just handing the keys to the kingdom over to Marcel Reed is a long-term mistake. He said he thinks it was smart for Sark to stick with Quinn and avoid trying out the shiny new object when Quinn struggled and stick to a plan and work towards a plan with confidence. I agree with the Ag and, I suppose, with Sark. (He wishes Elko had done the same with Weigman and that Weigman will go to another school and turn out to be a better QB than whatever A&M trots out for the next 2 years, a'la OU/Oregon Arnold/Gabriel.)
Do I, personally, want Arch to play? Absolutely, but it's for reasons beyond what is most likely to produce the best results overall for the team in the short/medium term (all we have remaining for this season). I want Arch to play for aesthetic and emotional reasons, for fan reasons.
My brain recognizes that we have a coach who is intelligently managing a team/roster and I trust that management.
Quinn is our QB, warts and all, because he is pretty clearly the better option in terms of winning the football games ahead of us. As cool as it would be to know Arch was starting and then start building stories in our heads about how he's going to be some hot-tempered, dynamic, play-making god, that's really just us having a fun time inventing stories in our heads.