I ask here: is it simply because of the way we choose to describe the “elementary” objects of the physical world, which happen to be much smaller than we are?

We are generally forced to investigate this elementary world by devising and interpreting experiments in which its constituents collide and scatter among themselves. An example is the way the position of an atom might be measured by projecting electrons at it and observing how they are scattered. We are forced to use such a clumsy method because we need small tools to investigate small objects. But this way of measuring has the complication that the investigating tools affect the object being investigated; they belong to the same milieu. It’s rather like psychology, which is imprecise because it involves humans studying humans.

One must then expect that quantities extracted from the elementary world will vary from one experiment to another, and that only statistical results will be obtained (in the example mentioned above one might get a blurred picture of an atom or a bell-shaped distribution of its measured positions).

We use the language of mathematics to quantitatively describe experimental observations, and this language has many dialects. Suppose it is decided to use Fourier methods to analyse the bell-shaped position curve. It then turns out that component waves, interpreted statistically as

the probability of the atom’s presence, can serve to analyse the bell-shaped velocity curve. And, provided their wavelength is made inversely proportional to momentum, statistical measurements of position and velocity can both be concisely described by the same mathematical dialect.

If a choice has been made of a statistical wave-dialect to describe the elementary world, one should persist with this choice in elaborating descriptions and one then obtains what we call quantum mechanics. But this circumstance, which we ourselves have contrived, does have a downside; it can encourage folk to endow physical phenomena with the properties of the mathematical tools they use to describe them.

The moral of this argument is that we should not read into quantum mechanics more than it contains. We need not ask whether atoms and electrons are "really" waves or if they are "really" particles. The wave-particle duality is not a mystery; question like those at the top of this post are just inappropriate. All we can do, for our own purposes, is to ephemerally described nature using one or other mathematical dialect. We cannot further "understand" it, or discuss what the elementary milieu "really" "is".