I have rarely been so happy as when I looked at my finished bike for the first time and thought, "I did this." It was a big project for someone who had never done anything like this before, and who considers himself mechanically disinclined. But, I'll be danged, I did it. The whole project came out exactly as I imagined. I now have a bike that works better (like new, in fact) and looks better, and I did every step of the process myself. I learned how to cut and install new cables, adjust a Sturmey-Archer 3-speed shifter, make fine adjustments on caliper brakes, sand, prime, and paint a bike, grease and reassemble the crank, headset, and axle bearings. I took my time (boy, did I), and I made sure that I did every step of the process just the right way. I documented everything with photos and meticulously bagged and organized each part I took off. In short, although it took me four months to do it, I did exactly what I set out to do.
I don't share all this just to feel good about myself (but, heck, I do!), I share it to make a point. Whether it's fixing bikes or cars (preferable bikes), home improvements, gardening, cooking, art projects, crafts, whatever, if you do it yourself you gain something in the doing. Not just the result you were shooting for, but a sense of accomplishment, a sense of pride in workmanship, and a new set of skills and experiences. If you take a chance, try something you thought impossible, you might actually accomplish it, and although it sounds a little trite, there is no better feeling in the world. In the process, you gain a little confidence, a little independence, and ultimately, I think, a better sense of yourself.