Some people are not human?

In ultimate reality things, people, beings, entities don't exist. You are stuck in concepts.

There exists only seeing, hearing, smelling, tasting, feeling and thinking and nothing more than that (except Nibbana).

Your question is just mental formations, just be mindful of the thoughts and your own reactions to it. Don't get caught up in concepts.

As my teachers teacher said: Delusion focuses on concepts. Wisdom focuses on Ultimate Reality.

I doubt regarding the six realms as 'physical reincarnation' can explain the statistics of people because the Pañcagatipeyyālavagga of the Samyutta Nikaya says only a few from each realm will attain the status of "human".

If we read all of the very short suttas in the Paṭhamaāmakadhaññapeyyālavagga until the end of the Pañcagatipeyyālavagga, we may possibly gain the impression the word "human" does not refer to something biological & reincarnated but instead refers to something mental & behavioral. The very first sutta here, titled "Not Human", says:

In the same way, the sentient beings reborn as [having comparative status of] humans are few, while those not reborn as humans are many. Why is that? It’s because they haven’t seen the four noble truths. What four? The noble truths of suffering, its origin, its cessation, and the path.

The strong impression above is the word "human" refers to "having seen (diṭṭha) the Four Noble Truths".

Again, suttas, such as SN 56.47, give the strong impression the word "human" refers to a mode of conduct rather than to a biological state from reincarnation. SN 56.47 says:

Sooner, I say, would that blind turtle, coming to the surface once every hundred years, insert its neck into that yoke with a single hole than the fool who has gone once to the nether world would regain the human state. For what reason? Because here, bhikkhus, there is no conduct guided by the Dhamma, no righteous conduct, no wholesome activity, no meritorious activity. Here there prevails mutual devouring, the devouring of the weak. For what reason? Because, bhikkhus, they have not seen the Four Noble Truths. What four? The noble truth of suffering … the noble truth of the way leading to the cessation of suffering.

There are many suttas similar to the above, such as AN 6.39:

it’s because of deeds born of greed, hate, and delusion that hell, the animal realm, the ghost realm, or any other bad places are found.... it’s because of deeds born of contentment, love, and understanding that gods, humans, or those in any other good places are found.

Iti 93 gives the impression the lower realms comprise of "mortals". The Pali here is "macca", which means "a man"; and "pajā", which "this generation of people" or "mankind".

The fire of greed burns a mortal (macca), lustful, infatuated by sensual pleasures; while, fallen in the fire of hate, a person kills living creatures; and, bewildered by the fire of delusion, they miss the teaching of the noble ones. Not recognizing these three fires, people (pajā) are caught up in identity.

They fill the ranks of hell, of birth as an animal, or of demons and ghosts, not freed from Māra’s bonds.

More relevant suttas can be read at this link: The five realms in the here-&-now.

While most Buddhists and many scriptures describe the realms as "physical", there are also suttas that describe the realms as "psychological". When the realms are regarded as psychological, illogical questions can be answered more logically & less speculatively.

Do they have to come from the souls of insects, reptiles, rodents, and other animals?

I have encountered talks that mentioned that there might be a mass transmigration from the animal (or beast) realm to the human realm. Considering the mass destruction of natural habitats of wild creatures and the extinction of many species in the past few centuries, this postulation may not be totally baseless. But this is beside the point. Regardless of which samsaric realms we are talking about, there is really no such definition as good or evil paths because it is all karma.

The Buddha pointed out that in our endless journey in samsara, we had experienced and taken on many existences/roles from kings to beggars, from devas to hell beings (see the Jakata tales for some stories of the Buddha's and his disciples' past lives as animals and other beings). Understanding this, we should be compassionate to all beings as we had been in their shoes and they had been in ours whether in the past, present or in the future. You may think you will never become that “not human” person you described. But there is no certainty in samsara except change, we have inevitably been the best and the worst of ourselves at some point in this long journey.

I recalled reading in the sutras about eras of wheel-turning monarchs (cakkavatti) and past Buddhas where the human population were very large but these eras were characterized by morality and virtues. My observation is that our era is characterized by the quest for freedom of desires and not the search for freedom from desires. You can see how society celebrate selfishness, ruthlessness and cunning intelligence as qualities necessary for success in life. Therefore, it is not surprising we see such qualities in our leaders (e.g. a certain ex-President of a powerful country who is rich and influential and whose mere words could incite a riot).

Can the Six Paths correctly explain it?

In short, my answer is no. What we are experiencing now is not only influenced by our past karma but also a result of our present choices and decisions. Unfortunately, we do not have a lot of good leadership models whether in politics or businesses or societies. Consequently, we had set up systems and processes that encouraged a winner-takes-all mentality. Look at the CEOs of huge multi-national companies and the leaders of large democracies. See how many aspires to fill those positions because they and their cronies can reap huge rewards if they succeed. This results in the poor getting poorer and the rich becoming richer. In such an environment, it’s no wonder those who are selfish, ruthless and cunning will excel just like in the animal realm. Measures had been taken to curb such detrimental winner-takes-all behaviour e.g. restricting the leadership term of a country to 2 or even 1 term. But I can’t help but feel it’s all patch work ala whack-a-mole approach with no effective long-term solution.

Some Buddhists had argued we should prioritize on attaining enlightenment before thinking of helping others. Their argument is that if you are drowning, you can’t even save yourself; how can you save others? Personally, I feel we should do more as Buddhists by proposing better and more holistic solutions that ensure human society progress in a more humane and sustainable direction if not for ourselves then for future generations of Buddhists. Who knows, we could be one of these future Buddhists if we fail to progress and come back again. We would not want to find ourselves living in a future world filled with strife and conflict, environmental pollution and climate disasters; where the rich and powerful takes the largest portion of resources while the poor eek out an existence worse than that of an animal.