Why humans tend not to use reptiles, amphibians, small mammals, non teleost aquatic vertebrates, most invertebrates and carnivores as a food source? When most were hunters and gatherers, they were eating all of them, like the Australian Aboriginals, but after the invention of agriculture and the stable presence of fatty, nutritious ungulate meat, their consumption nearly stopped, continuing only in some areas were some species were in abundance, like the Uromastix of the Middle East or the iguanas of Central America, or where the population was too high, like in China and Aztec Mexico. Some were adopted as a custom after a past period of necessity, like for example the consumption of tarantulas in modern Cambodia from the period of great famine due to the recent unrest, or the relatively greater variety of hunted animals in the American South, like opossums, raccoons, rattlers, snapping turtles and alligators, which would never be considered as food by Europeans. Even then, they were just some selected species (usually herbivores or non-threatening looking animals – turtles were eaten more than other reptiles in most countries -, and their consumption, with some exceptions, didn’t reach the levels of the consumption of more acceptable meats. Most of the time their consumption is linked to lower socioeconomic levels, remote rural areas or they are not so high-class meals. For example the uromastix lizards were mainly a food for bedowin nomads, whilst town folk did not eat them. Insects, lizards, rats, fruit bats and other smallish animals are hunted by poor sectors of the population of many tropical countries, but wealthier people usually don’t eat them. For that reason, usually when those regions get westernized, these foods fall out of favor. Then comes the conservation and public health rhetoric, to rationalize the avertion of westerners to the consumption of such animals. They are regarded as bush meat, and all of them are treated either as threatened or disease carrying animals, even if they are a heterogeneous group, with endangerement and disease risk varying much between species.

Sometimes though the consumption of some species can be accepted and promoted as a high class or exotic food. For example both frog legs and snails are esteamed by some, yet they remain just that, esteamed high class foods, with very limited daily consumption, even though these animals are widespread in the environment.

Being small and difficult to catch doesn’t seem as a satisfactory explanation. For example truly little birds of the size of a common sparrow are eaten in many western countries, even though they are difficult and time-consuming to catch, and their meat is minute. Yet a reptile or mammal of the same mass would never be considered edible. It is to much of a coincidence that most animals of these categories evoke negative emotions of fear, aversion and disgust in many persons, and even science until recently lumped them in taxonomy and didn’t study them so much (compare studies made on avian and mammalian intelligence for example, with those on reptilian) intelligence. Negative emotions might had developed after these animals stopped being eaten.

This category of animals includes: most reptiles, amphibians, small mammals under rabbit-sized (mice, rats, squirrels, hedgehogs, mustelids, bats, shrews, moles, opossums, etc), nearly any insect and terrestrial mollusk or worms save for snails in some regions, many non-standard looking teleosts like eel, catfish, pufferfish, sea horse, etc, non teleosts like sturgeon, lungfish, bichir, chondrichthyans save for very few species in some regions, etc, aquatic tetrapods like sea turtles or cetaceans, and many marine invertebrates, like mollusks, arthropods and echinoderms.

Also, there is a general aversion of humans against eating carnivores. Of the domestic animals, dogs, as omnivores, might be eaten in some parts of the world, while cats, as true carnivores, are eaten much less. Even omnivores are today raised primarily as herbivores, with regulations of many western countries forbidding the feeding of animal products to pigs fore example, ostensibly for disease-prevention reasons, but it might as well be the scientific refurbishment of an old food taboo. Chickens likewise are denyed live prey in intensive farm conditions, even if they like to hunt them, as they have evolved to eat them. As for carnivores, I don’t know of any culture hunting them systematically as food, even smaller, less dangerous species like foxes or weasels. The same applies for birds of prey, waders, seabirds, scavengers, and other species of bird clearly shown to hunt other animals. All these above animals might be eaten for perported medicinal benefits, but never as a stapple meat.

The human aversion towards such animals and their meat was so strong, that many times it was codified into various religions as sacred law not to eat them. For example In ancient Egyptian religion, in Judaism, in islam, in some branches of Christianity, in Hinduism, in Zoroastrianism, there are rules against eating some or all of the above animals.

Why most humans do not eat those animals?

that isn't so much a question its more like an essay!

To summarise if I have understood you correctly you are asking why different human populations over time and regionally have adopted different food likes/dislikes and eating habits.

The answer unsurprisingly is largely environmental and societal and has almost nothing to do with genetics. foods go in and out of fashion and that is just as true today (and variably across the world) as it was in ancient Egypt, Elizabethan or Victorian times. I am not sure there is much else I can say that is helpful other than to note that those societal factors will not apply to lower species where the main aim is to consume enough food to stay alive, procreate and survive the winter.