When I was little, my friends and family told me they liked my stories. Whenever they read something I was writing, they would always say, "when are you writing more?"
When I started college, my classmates did the same thing. My teachers, along with giving me constructive criticism, told me that I was a good writer.
These teachers pushed me harder as I finished my bachelor's degree and went on to a master's program.
These teachers didn't bat an eyelash when I told them I wanted to go on for a Ph.D. in creative writing.
The writing group I'm a part of, while giving me constructive criticism, tells me they like my stories. And I don't think they're lying, because they like some a lot better than others.
I guess that's what makes me feel my writing is worth reading. Or maybe it's just what reassures me that my writing is worth reading. And even though I've gotten mostly rejections for my stories so far, I still get the occasional personal rejection that says my stories are "well written." So I can have at least a crumb of confidence amidst the rejections. (To be honest, I haven't written anything new in a year, and looking back on this stuff with the eyes of someone who's had another year of grad school, the stories needed some serious help before they were going to be publishable material, so I don't really take even the form rejections as any indication that I'm not worth reading.)
Plus, I like reading the sorts of things I write, so I figure someone out there's going to feel the same way about it.