Because, argues the Kenilworthian, our losses constantly remind us of our lack of knowledge about the game, and this then causes us pain or at least curiosity - and so we come back to the game again and again to learn more. And of course, the more we learn, the more we know how ignorant we truly are, and so the cycle of knowledge, knowledge-gaps, pain, curiosity, learning, knowledge!, knowledge gaps repeats and repeats.
Could well be. "Of chess it has been said that life is not long enough for it, but that is the fault of life, not chess," said William Napier (commonly attributed to Irving Chernev) and, indeed. If we knew we could master chess with, say, five years effort, would we bother? Few do with Connect 4, by comparison for example. And didn't Bobby Fischer say we should all play Chess960 because the middlegames of chess are effectively solved? Could a lack of the pain and the curiosity caused by knowledge-gaps be why he is no longer playing? (As an aside, however, I would be more inclined to speculate on Jan Hein Donner's argument that: "No one is as lonely as the world champion" in any attempt to answer this question.)
On the other hand, the comments here suggest various other interesting reasons. And I'm not sure I can apply all this to myself very convincingly. I started playing socially as a kid after school for fun, and by around my teens began to appreciate the game sufficiently for its own sake - as a thing of beauty, drama and excitement. No doubt curiosity and competitiveness were there too. But when answering the question "Why do I play chess?" I am more likely to formulate some watered down version of Hans Ree's explanation: "Chess is beautiful enough to waste your life for." Ree isn't the only chess player to stress this side of the game of course. "If you have never seen this study before and fail to find it exciting," wrote Levitt and Friedgood about the study by V Korolkov on the left for instance (1st Prize, Lelo 1951, white to play and win, click to enlarge) "our only advice is to give up the game straight away. You will have no future in chess!"
Life is full of questions and attempts at answers and then more questions. But only one more for this post. Why do you play chess?