1) Without publishing, you won't ever find your audience. There are people out there who will both love and hate your writing and the things that you write about. In many ways, I think it's as difficult to connect with an audience as it is to find your soul mate. However, if you keep plugging away at it, the chances improve that someone that is engaged with your writing will eventually stumble across it. I know because this has happened to me. You've got to put yourself out there in order to be found.
2) Without publishing, you will never be finished with your project. I think hitting the "publish" button is important for a writer, because without doing so your manuscript/project will linger in this weird space where you can always find something wrong that needs to be fixed. You may even pick at it, finding some word that you can't believe you used and replacing it with another or a handful of things that you might view as mistakes but no one really notices or cares about. The act of publishing gets rid of all that by saying, "I'm finished."
3) Without publishing, you will never get an accurate sense of how good or bad of a writer you are. Everyone turns to their friends and family for critiques, and these are generally the worst kinds of reviews because they are heavily biased. I think that the only opinion that matters is one from your target audience, which is why it's important to a writer to maintain contact with these people once you connect with them (newsletters, blogs, and publishing more books are all good ways to stay in touch with your target audience once it has been found).
4) Without publishing you won't make any money. You have to get your product out there, and if you want to be taken seriously, publishing is one way to do that. By taking the final step, you are asking your target audience that your labor of love is actually worth money. How much you actually get back is going to vary from author to author. But that first dollar actually feels pretty darn good.
5) Publishing shows people that you can finish a project, but it also makes writing the next book easier. It goes without saying that once you've done something, it's much easier to repeat. You also get better at stringing words together (in general) as with any craft. Even if your sales end up really small, the fact that you published anything at all is a success in my book.