Why is baklava never kept in the fridge?

Baklava's texture is a balance of three things: paper-thin pastry, clarified butter and hot syrup. Butter begins to set below roughly 20°C; in the fridge that setting glues the layers together, so the slice crumbles instead of cracking.

The syrup has the opposite problem: sugar loses solubility in the cold, crystallises and settles into the pores of the pastry. Reheating a chilled tray does not undo the damage, because the pastry has taken on moisture in the meantime.

The practical rule: keep baklava at room temperature on the day you buy it, with the lid left slightly open. If it must be stored for longer, a freezer is better than a fridge, and it should thaw slowly at room temperature.