We humans have gone to war with certain animals since prehistoric times. Over the millenia, the targets have changed, but for each generation there has been a widespread belief that things would be better if we could wipe out one or another animal species that is bothering us, interfering with our well-being or otherwise preventing us from doing what we please. Simply controlling the population of the bothersome creature was probably a less desirable outcome than complete elimination so as to put the problem to rest. Also changing over time was the type and proximity of the animal we have sought to rid ourselves of.
Even before the emergence of agriculture, the humans that walked the earth hunting and gathering undoubtedly feared certain animals which were either predators (e.g. saber tooth tiger, dire wolf) or that otherwise inspired fear for some reason (snakes, crocodiles, other reptiles). Superstitious beliefs about certain animals being evil persist even today and in certain cultures it is taken for granted that one must kill any of a species which crosses your path.
As humans began growing crops, breeding animals and remaining stationary, a different but related set of creatures posed a threat which was met with eradication efforts. Carnivores such as coyotes, wolves and wild cats may have begun to fear man but found sustenance in killing livestock while groundhogs, mice and rats threatened plant crops. In either case, the early farming communities spent a lot of effort not only not only to control but ideally eliminate these animals from their turf for good. I say this because it took some effort away from farming to battle these four legged creatures and it would likely have suited folks just fine if they could finish the job and get rid of these "intruders" once and for all.
Over the centuries, trade and technology grew alongside civilization and soon agricultural man discovered advanced methods to fight the insects that had ravaged his crops from since the beginning. Chemicals and powders were developed that could wipe out certain insects (and unwittingly, others as collateral damage) with a minimum of effort, especially after the use of airplanes to administer this form of biological and chemical warfare on animals. Poisons also proved useful in the longstanding battle against mammalian pests as well, making it much more efficient than hunting and trapping, although bounties and other economic incentives made the latter very efficient.
The battle to eliminate pests gradually moved inside the home from farm and field. Technology permitted the emergence of manufacturing for retail customers and soon companies were marketing products for ridding one's household of flies, cockroaches, mice, ants and all manner of animal visitors. Not knowing anything about ecology or the health of the planet, housewives and their husbands in the mid 20th century would have been just as happy to remove these home invaders not only from within their four walls but from the surrounding lawns and the entire countryside.
Soon the war against all animals that weren't human, livestock or house pets turned to the smallest of creatures--microorganisms. It became affordable and easy for people to attempt to rid their homes of bacteria using chemicals available at retail stores. We began to see anti-bacterial wipes and sprays which purported to clear your kitchen or bathroom of all living organisms, leaving a sterile (and by implication healthier) home to live in. Soon enough it came out that a number of illnesses and allergies prevalent in American youth were due in part to the sterilization of their environment as infants. Still, when advertisement portrayed bacteria as evil beings many persisted in a desire to remove all organisms from their environment.
There was even a lawn care products company which promised to eliminate insects and other invertebrates from the top 12 inches or so of your lawn so that your children would not be threatened by these evil beings.
And finally, our eradication efforts have turned to the internal bacteria which all of us host by the billions in our gut. The battle moved from forest to farm to home and finally, inside ourselves. If you told (or better yet showed) the average person about the billions of microorganisms inhabiting his body, he might look for a way to sterilize every cavity and chamber within himself.
So we humans have moved the battle against animals from forest and field to farms, our homes, kitchens and baths and finally into our bodies. In recent years we've all heard of the drawbacks of the overuse of antibiotics both in hospitals and agriculture. Instead of eradicating all bacterial (a foolish pursuit) we have enabled only the strongest to survive. Today our antibiotics are nearly worthless because of this effort.
Many also are beginning to realize that the elimination of certain animal species outside of our homes leads to unintended and undesirable consequences. Deliberately getting rid of any single plant or animal species is foolish but few people notice.