Proper double fan gluing means shuffling the papers together to get a nice edge, standing them on edge so the spine is upward and somehow clamping or bracing it (ideally, it's between two boards in a laying press, but there's a lot of ways to make it work) and then pushing the spine to one side, fanning out the spine edges so a bit of the side is exposing. Spread glue, then push the spine to the other side the same amount, exposing the other slight side of the page and reapply glue. Then straighten the spine.

This will leave between the pages for, ideally, less than 1/32nd of an inch or a quarter millimeter, which will vastly improve the strength of the glue's attachment to the pages without significantly impairing one's ability to open the pages mostly flat.