I like to keep all of my old art up for people to see, unless it is something I really don't like. I keep it up because I want people to be encouraged to continue working on art. Because we don't all start out as really good artists, it takes time and practice. I didn't start out at the level I am at now, no one does. I don't think anyone should give up on art because they think they could never reach the same level as another artist.
Keep going, you can only improve from here.