I stress, good answers by actually doing research and/or thinking about it. I have my reasons but I’m really interested in knowing yours.
Short answer: It makes me feel good.
Longer answer: Not only do I like to write good answers for Quora but whenever I write answers or papers or articles I like to do an excellent job of it. It makes for better reading, and therefore more satisfaction on my part. Also, learning all I can about the world and sharing this information gives my life meaning, but unless it is well-written, no one is going to read it and I feel my life is wasted.
As a by-product, it seems some people get help from some of my answers. That also makes me feel good but nothing rivals the satisfaction of thoughts well organized and articulated. I suppose that sounds pretty cold and impersonal, but it’s the way I am. Whether anyone reads them is secondary, though of course it provides an incentive to keep on if I know people are reading and enjoying.
I think that covers the main areas of what motivates me to write for Quora.