That's a great question that many people are not even asking.  What is this ubiquitous material that's in our lives every day and is part of a global waste crisis in many places on earth?
Modern-day plastic has been developed over the last 170 years or so into the different types we see today.  It started off as a humble, nobly-purposed alternative to ivory called celluloid (generally, over time it had different names according to the inventors) in the mid-1850s through the early 1920s when more and better types of plastic were discovered.
In the 1950s we began to see the plastics still used in today's packaging: polypropylene, expanded polystyrene (styrofoam), PET, HDPE, and others.  These plastics are essentially the ones we still use today!  Though some formulations have changed due to health and environmental concerns.
More technically, plastics are polymers which are larger groups of molecules composed of linked monomers.  Plastic is a synthesis of several elements, often products of natural gas, crude oil, and salts (with other additives depending on the purpose of the material).  For instance, PVC stands for Polyvinyl Chloride, the name reflecting the use of Chloride which is a common agent in plastic.
Just as plastic once provided a substitute for a dwindling, precious, and cruel resource in ivory, now we should be searching for a substitute for the dwindling precious resource of our time: environmental health.
Suggested reading:
Plastic: A Toxic Love Story by Susan Freinkel
US Generates More Plastic Trash Than Any Other Nation
Molecules Bio


There are plenty of use cases where plastic is an ideal material.  Like many other things, if used and managed properly it does not pose a serious and urgent problem to the lives of people on Earth.
As you already know, however, plastic has been used and used and used.  Overused.  Not only has it been overused, it has been done in a careless fashion that acclimated practically every culture to single-use disposable plastic.  Now, decades into the future, we discover that plastics have just been accumulating in our waterways.  Our marine life, including fish and other sea animals that we eat, are eating plastic and suffering due to plastic in their bodies.  In turn, we suffer the loss of these creatures as part of our food source and the quality of our lives diminish as populations struggle against environmental toxicity.  The animals that live up the food chain such as sea birds also end up ingesting plastic, and on and on.
The problem with disposable plastic is that it's window of use is extremely small yet it's ill effects are insidious and long-lasting... and quiet.  Less fortunate regions around the world suffer under the waste of the more affluent, their rivers, lakes, oceans, beaches, awash with plastic waste in various stages of degradation.  All life on earth is suffering in one way or another due to the immense level of plastic waste now present and more waste is being generated every single day.
What about recycling?  Unfortunately, recycling has not been the promised solution to making plastic more circular and less wasteful.  According to an article by environmental researcher Laura Parker, 91% of plastic waste has not been recycled after all (source: https://www.nationalgeographic.org/article/whopping-91-percent-plastic-isnt-recycled/) and recycling continues to be an ineffective solution.  Some countries have turned to incineration, but those facilities are few and require a lot of heat to burn without releasing toxic gases to the environment.  Recycling does help, but it is not even close to addressing the magnitude of the crisis.
Waste Management