I can try to provide a (late) serious, long-ish response.

First of all there is no "the plastic atom" they are chemically more diverse than anything in computer-land. So the concerns of polycarb plastics have no relationship with polyethylene or teflon or whatever other than coincidentally having been industrially developed around the same decades so people call them all plastics, although its actually worse than calling anything green a plant and assuming they're all the same.

Here's your analogy: Plastics are tangled up strings. Like a crazy nanoscale 3-d composite. The strings are mfgr in place by dumping a bunch of wanna-be string pieces and crazy reactive hyperactive catalyst in a form and then waiting, maybe heating, to convince the catalyst to bond wanna-be string chunks into a long string.

The mechanism or turning pieces of string into a long string is surprisingly common and boring, which is the source of the whole problem. You have a chunky molecule with a finger or whatever sticking out containing a double bond. Just a plain old boring double bond like you'd find all over the place, like unfortunately in your innards. The crazy catalyst has the unusual ability to snap open double bonds and fall off to repeat maybe a few thousand times. Then the opened double bonds sometimes snap right shut, but sometimes grab a neighbor.

Think of a clown car with 20 people squashed into it, clasping their left and right hand together, and "magically" their hands unclasp for a moment, maybe, and due to crowding, their hands snap shut on a neighbors hand instead of their own. Now instead of having 20 separate clowns in a clown car, you got a conga line of 20 attached clowns wedged into place and you can't remove just one anymore because they're all stuck together. They've polymerized into a car shaped brick with a molecular weight of about 20 clowns. So now you know why some plastics are industrially sold based on molecular weight.

The "trick" to making plastics is making a shelf stable substance, preferably liquid-ish, that won't spontaneously polymerize, but has crazy molecule sex with all its neighbors at the drop of a catalyst hat. The catalyst is like a little monster than hands out to everyone little molecule-condoms coated with superglue instead of lube. (don't take this all literally, but figuratively it kinda works) Its actually quite tricky chemistry which is why it took till the last century to really kick off plastic production "for real" rather than just screwing around.

Plastics stereotypically, on average across the field, are super boring biochemically. Pure polyethylene is about as chemically exciting and reactive as asphalt, for example. Probably because it vaguely resembles asphalt chemically, you can make synthetic oil out of little bits, and polyethylene is close to what synthetic asphalt would look like. Kinda. Unpolymerized polyethylene is just a simple flammable gas, a very close cousin of propane / butane. The reason why nobody owns a ethylene cigarette lighter or has an ethylene grill in their backyard to grill burgers is it all goes into plastics not lighters and grills... So the world is full of really boring plastics. But not all plastics are boring.

Unfortunately, BPA makes a totally awesome and non-biologically reactive plastic once it cures and links up to the neighbors in a big chunk, but by itself, uncured, its fairly nasty stuff. It really wants to grab hold of another molecule, which is awesome if it successfully grabs hold and never lets go of another BPA molecule, but kinda bad if it mistakenly grabs onto your DNA (or whatever) like a bear trap.

There are also interesting "green" implications such that if BPA based plastics ever decay, its just like dumping a tanker car of monomer out in the landfill. Kinda nasty if it ever happens. On the other hand, never breaking down is kind of ecologically nasty too. Generally speaking the "green" plastics like PLA or PE have non-toxic monomers and are not nearly as durable as the "non-green" plastics like polycarb family, speaking generally, etc.