What can cause teeth to separate?

Bad habits. Bad bite, extra spacing , bad habits or porr peridontal condition are the main causea.
Light constant force. All that is requires to move teeth is a light constant force or vibration. This is how orthodontics works! gum disease, more specifically periodontitis, can also cause teeth to move and shift because the foundation has become damaged and under biting forces teeth can separate.
Drifting teeth. There are many things that can cause teeth to drift. The most common one is loss of bone support from periodontal (gum) disease. Other causes are loss of teeth with resultant bite collapse, an unstable occlusion, parafunctional habits such as biting on pens, post orthodontic treatment and not wearing a retainer, infections, cysts, and tumors.