long story short, transparent plastic containers tend to imbue their contents with a chemical called bisphenol-a (aka bpa), which is a compound similar to estrogen which may impact human physiology in a wide array of ways[0], or chemicals that are structurally related that aren't well studied but could be similarly damaging[1]. this applies to all transparent plastics and isn't specific to aeropresses
[0] https://en.wikipedia.org/wiki/Bisphenol_A#Health_effects
[1] http://www.motherjones.com/environment/2014/03/tritan-certic...