The reason not to go public is that Wall Street has a tendency to force your company to stray from its mission in for of faster growth. Case in point, southwest airlines: You can't be the most loved airline if you're going to throw out basically everything that your customers liked about you to begin with. But some activist Wall Street investor believes they'll grow faster by being more like other airlines. Are they right? Maybe. Time will tell. Other investors seem to believe so. If they were private, and closely held by people who shared that vision, they wouldn't he had to do that. Their CEO didn't want to until a hedge fund forced his hand.
I work for a company that is privately held, and it's nice not hing to care even the slightest about the monetary growth treadmill in the quarterly reports. Rather, we get to define our own measurements for results. We don't answer to Wall Street. Same thing applies if you work for a nonprofit (and don't make the mistake of assuming that nonprofits aren't profitable to their stakeholders -- it isn't even remotely true.)