I'm not really sure what OP is asking here, i.e., are they asking in what way was it the symbolic end of the "sixties" as a social and cultural movement? I'm not familiar with any prevailing opinion that it necessarily was, except for the fact that it happened during the latter half of 1969. Part of me is suspicious of the question as a whole, as it seems to imply that this statement, that Woodstock was a logical end of the 60s, is true, and that we should provide evidence to prop this supposition up in some way.

For the sake of argument, however, I'll try to unpack this a little. If one were to say that the Woodstock Music and Arts Fair of August 1969 was the zenith of the 1960s counterculture movement, you might be able to argue that, yes. Both through the event itself, and the documentary film that followed, the festival sort of defined itself as just that: the culmination of the counter culture's "movement" (if you could call it that). It presented itself as the embodiment of the "turn on, tune in, drop out" ethos that had been percolating alongside anti-war activism, a rising consciousness in social rights issues, and a massive, radical reevaluation of the youth culture's social identity. Both the New York and (especially) S.F. music scenes were deeply rooted in this nebulous cultural movement, so Woodstock became the focal point for it all right when it seemed to peak. There were other rallying points before this, don't be mistaken (see the Monterey Pop Festival of June 1967 for another example), but Woodstock became the largest, and ultimately most visible "moment," if you will.

There were a lot of reasons for this, from the fact that Woodstock had some of the biggest musical acts of that period booked, to the shaping of the narrative through the subsequent documentary, right up to the way that the festival organizers and participants talked about the event at the time. They made it out to be the grand result of a movement that was above materialism, conservative-minded politics, etc. by talking about how it was a "free" concert, and "three days of peace and love." People who were actually there, either as organizers, performers, or spectators (if speaking honestly, anyway) will tell you a different story, though. They DID sell tickets (although many did just jump or go around fences to get in for free), the performers WERE paid, and there were plenty of issues both before, during, and after the event. Check out Bob Spitz's book 'Barefoot in Babylon' for more on this.

Going back to OP'S question, I don't know that anything I've read definitively uses Woodstock as some kind of high watermark for "the sixties." Many have written about this concept (Hunter S. Thompson did so masterfully in 'Fear and Loathing in Las Vegas') but I've yet to see a historian make a hard case for Woodstock as the seminal event that defined the end of the movement. If anything, it was (in my own opinion) a perfect example or encapsulation of the 60s counter culture in that the event was half baked, half thought out, handled in an amateur fashion, yet came off and succeeded in spite of itself, if only for a brief, flickering moment. That's the 60s counter culture movement for you.

If you want to look at an event that many professional and cultural historians DO point towards as the "end" of the 60s, look no further than Altamont (Dec. 1969).