a look at aerial imagery (http://maps.google.com/maps?q=the+golden+gate+bridge&ll=37.820226,-122.476444&sll=37.775000,-122.418333&spn=0.029822,0.054957&sspn=0.120488,0.231400&t=k&hl=en) and a side view (http://www.truscott.id.au/our_life/albums/US%20Holiday%2004_05/IMG_3515.JPG) make it pretty obvious why: that's both where the suspension cable is at its lowest (which is what looks like the center of the bridge when you're on it) and it's above the deepest water.

it's also easier to get over the railing there because it's an access point for employees to get up onto the cable.