BPA is not a plasticizer. Plain and simple. BPA (bisphenol A) is not a plasticizer.
BPA is not an plastic additive. Plain and simple. BPA is not a plastic additive.
BPA is not added to plastic to make it harder. Plain and simple. BPA is not added to plastic to make it harder.
These thoughts that have become so widely spread across the internet that not only are the mainstream media falling for them (1, 2, 3 and 4), but scientists are publishing papers and books making these mistakes as well (1, 2 and 3).
Let me try and rectify the errors. Plasticizers are compounds that are added to an existing plastic to make it more plastic-y (meaning able to undergo irreversible deformation). They are commonly phthalates, but they can be other compounds as well. BPA on the other, is a monomer, which when reacted with other monomers produces a plastic. It does not change the properties of an existing plastic - it's one of the chemicals that reacts to form a new plastic.
In order to effectively plasticize a plastic, plasticizers need to be added in significant amounts, sometimes as much as 50 wt%. That's why an IV bag (extremely soft) and a white drain pipe (extremely hard) can both made from the same base material - PVC. With so much plasticizer in the plastic, it is readily apparent that some of it could leach out, hence the concern about potential hazards from the leachate. But there are also concerns about BPA leaching out of plastic as well. While BPA can and does leach out of plastics, it is unreacted BPA that is leaching out. (Polymerization reactions are seldom able to achieve 100% yields due to a combination of factors, including very high viscosities reducing reactant diffusion rates.) The amount of unreacted BPA is very small, far less than 1%, and far less than the concentration levels of any plasticizers. I think the fact that both phthalates and BPA can diffuse out of plastics is the source of much of the confusion.
The misstatements that I opened this post with have almost taken on urban legend status (and I didn't even cover the laughable "all plastics contain BPA" statement). I run across them far too often and from people that should know better. But expecting this post to change anything is like expecting a spitball to bring down an F-16.