Quoted:
Prior to 1945 the eagle on the presidential seal faced the arrows.
The official description of the seal does not specify to which side the eagle must face. It's gone both ways, depending on who's doing the rendering, in the past.
A bit of unofficial lore has sprung up about the wartime vs peacetime renderings vis-a-vis supposedly during wartime, the eagle faces the arrows, while normally it faces the olive branch.