So, it's 10,495 BCE and I'm on my way to Göbekli Tepe... wait, why am I on my way to Göbekli Tepe?

This is a great question that opens the door to an abyss that is nearly impossible to fathom. This is likely reflected by the numerous "comment removed" that represent the only answers to this question as I attempt to write something that will not be removed. In fact, it is noteworthy that someone regarded one of the comments to be so good that it was gilded - before it was removed!

So why is this? It is because we are left with speculation as the only way to imagine an answer to your question - or to the many other questions raised by this amazing archaeological discovery. Because this subreddit sometimes inspires wild-eyed imaginings and because Göbekli Tepe can be regarded as an enigma wrapped in a mystery (to paraphrase the expression), it is a topic that attracts speculation on a grand scale. Coincidentally, it also appear to have been a place that attracted attention on a grand scale when it functioned in prehistory.

To understand the nature of that prehistoric attention we must recognize what we know in absolute terms and what is speculation. Failure to differentiate between those two is a quick path to "Comment removed" - leaving us with a series of answers on /r/AskHistorians, lost to history and about which, again coincidentally, we can only speculate. We can regard the content of that long list of comments that have been removed as the equivalent to the answers we seek about Göbekli Tepe: we don't know a lot about the why of that place, just as we can only speculate about the content of the removed answers. I find all that to be frustrating as hell, but screaming about my frustration does not yield any insights.

So what do we know about this remarkable site? It took a lot of labor to assemble the complex, and given the deposition, it is clear that the site was used over time, with the replacement of older circles by new ones, which were constructed atop the others. All this was occurring when people were engaged in hunting and gathering and/or Neolithic-like domestication of plants and animals. It is, in fact, frustratingly near the point when people were fundamentally changing their approach to food gathering and production. Even the ambiguity of that dating causes more speculation than answers as scholars debate whether this is late hunter-gatherers or early Neolithic farmers. Damn!!! More questions than answers!!!

So what else do we know? The construction of this site took people a lot of time to build this site, and it appears logical to assume that a lot of people were "on the way to Göbekli Tepe." We cannot, unfortunately, be sure why that was. People are people regardless of the millennium, so we can speculate (as long as we acknowledge that it is speculation) that people sometimes spend their leisure time traveling to see remarkable things. It is also common for cultures to encourage travel for religious purposes. Göbekli Tepe is remarkable, so it is reasonable to assume that people went there because it was a remarkable place to see. It appears to have had some religious purpose, so it appears that people were going there not merely for sightseeing, but also to fulfill some spiritual, religious need. Even that, however, is speculation, and speculation is decidedly unsatisfying - often leading to even more speculation.

I find it particularly satisfying to know that beginning perhaps as early as the twelfth millennium before present large numbers of people were gathering to construct and then to visit a remarkable place. This is earlier than most scholars just a few decades ago suspected would have been possible. That's not speculation - it is genuine insight. Why they undertook this construction project and then visited the place is open to speculation, but it is almost impossible to avoid a religious/spiritual explanation. The specifics beyond that simple answer are unknown and unknowable because this is prehistory. Archaeology takes us to the brink of the abyss of knowing, but it cannot shed light upon the darkness within.

I have read speculation about how this site represents a transition from large animals/small humans in Paleolithic art to large humans/small animals at Göbekli Tepe. That's an interesting observation, but I'm not sure what that means largely because I cannot know if the prehistoric participants thought about that in those terms. The speculation behind this observation sometimes concludes that we are seeing a transition from a period where the world dominated humanity to a time where humanity dominated the world. Making that observation today is not unlike all the ink that has been spilled about the play "Hamlet." Literary criticism and even psychological analysis tells us a great deal about what the play means, but we cannot be certain that Shakespeare thought about his play in those terms. Artistic and literary criticism can give us new ways to think about landmark artistic monuments like "Hamlet" and/or Göbekli Tepe, but that does not mean that the artists behind those monuments saw their work in those terms. In the case of Shakespeare, we have some ability to gain some insight through written documents from his period (and yet there is much we do not know); in the case of Göbekli Tepe there is nothing of the sort. All that remains is a dark abyss that we are tempted to fill with speculation.

In short: great question; sorry, but no answer.

edit: Thanks for the gilding!