You might think it's because we give direction and light the way. Sometimes, but that isn't our primary role.
The word facilitation simply means to make easier. A facilitator removes the barriers.
Years ago there was a documentary that gave a wonderful example. It showed the process of moving a lighthouse. This historic lighthouse was too close to an eroding cliff and was going to be lost if nothing was done. They built a system of huge wooden rails that the entire structure would slide on. Then, just before they began pulling this multi-ton stone monstrosity to its new home, they coated the skids with Ivory soap. A small disruption in movement could spell disaster, so they lubricated everything.
A facilitator's job is to be the Ivory soap. The soap wasn't structural; it didn't become part of the lighthouse, but it kept the lighthouse moving. A facilitator doesn't become part of the team; if he or she does they loose their objectivity and effectiveness. The facilitator doesn't bring the solution. The facilitator removes the friction and makes it possible to get to the solution. A facilitator's primary job is to recognize the sources of friction and eliminate them if possible, and if they can't be eliminated completely at least manage them so they don't stop the progress.