I don't think I could ever pick "Never Have". It's by far the more depressing option.
The operative word in the poll is 'never'. You'll never have what it is you want, in either case. So, in the case of "Never Have", striving to attain it is the epitome of futility. It's not a goal. It's a cruel insult.
With the "Never Know" option you'll never find that one thing that you want, but you'll at least have the chance to find a few things you do like while trying to figure out what it is you want.
The same could technically be said about the "Never Have" option, but regardless of what alternatives you find you'll never be able to truly enjoy them because none of them are the thing you truly want. You'll forever have the comparison of the thing you're striving for. If anything, finding alternatives will drive home the idea that you'll never have what it is that you want, making the whole endeavor even more depressing. With "Never Know" you'll have to deal with the idea that the alternatives you've found aren't the thing you're looking for, but since you don't actually know what that thing is you have only speculation on how much better it could be. This can make it easier to accept the alternative for what it is without the constant nagging feeling that it's not as good as the one you want.
That's why, to me anyway, striving to find the desired unknown is a far more optimistic goal than trying to attain the thing you can never have. It leads to more open-ended possibilities of discovery than aiming for a single-target goal.