No problem should ever have to be solved twice.

Creative brains are a valuable, limited resource. They shouldn't be wasted on re-inventing the wheel when there are so many fascinating new problems waiting out there.
To behave like a hacker, you have to believe that the thinking time of other hackers is precious — so much so that it's almost a moral duty for you to share information, solve problems and then give the solutions away just so other hackers can solve new problems instead of having to perpetually re-address old ones.
Note, however, that "No problem should ever have to be solved twice." does not imply that you have to consider all existing solutions sacred, or that there is only one right solution to any given problem. Often, we learn a lot about the problem that we didn't know before by studying the first cut at a solution. It's OK, and often necessary, to decide that we can do better. What's not OK is artificial technical, legal, or institutional barriers (like closed-source code) that prevent a good solution from being re-used and force people to re-invent wheels.
(You don't have to believe that you're obligated to give all your creative product away, though the hackers that do are the ones that get most respect from other hackers. It's consistent with hacker values to sell enough of it to keep you in food and rent and computers. It's fine to use your hacking skills to support a family or even get rich, as long as you don't forget your loyalty to your art and your fellow hackers while doing it.)