Not everybody who lived in the area was exactly thrilled about the festival coming to town. We shouldn't judge them for that - imagine your town, suddenly filled with an additional half a million people screaming, shouting, taking drugs and not washing for three days. It's not unreasonable to be more than a little annoyed by that. The residents of Woodstock hated the idea. And that's why the festival didn't actually happen at Woodstock.
Although Woodstock was the original intended destination, the organizers just couldn't find a suitable candidate for a venue, so they tried to move it to Wallkill. The residents of Wallkill outright refused permission for the festival to be staged within their boundaries, so Bethel got to play host as the third choice. The name 'Woodstock' was kept just because it sounded cooler than Bethel.