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
That may be true, but unfortunately research is showing plasticizers of many varieties (including those used in "BPA Free" plastics), are endocrine disruptors.
[0] https://en.wikipedia.org/wiki/Bisphenol_A#Health_effects
[1] http://www.motherjones.com/environment/2014/03/tritan-certic...