I do agree it is unfortunate if some scientists, in TV popularisations or books, forget to remind their audience that this is all about models (usually highly successful and amply reconfirmed). Maybe it is this impression of certainty or arrogance that offends you. If so, I have some sympathy.
Now to QM and the Periodic Table:
Mendeleev, when he constructed the Table did so on purely empirical grounds: he ordered elements according to their atomic weight (increasing left to right and top to bottom, like lines on a page) and the similarities known at the time in their physical and chemical behaviour (which determined the lengths of each line). But why is there a block of two columns on the left, one of 6 columns on the right and one of 10 in the middle? And why do "alkali metals" such as lithium and sodium form ionic compounds in which they are +ve ions, while inert gases do not form compounds at all?
QM provided the answers. In QM, the electrons in the atom behave like waves. It is well known by musicians that if you twang a violin string, it will vibrate at a set of resonant frequencies, made up of a standing waves. You can excite the fundamental, or the 1st harmonic, 1 octave above the fundamental, or the 2nd harmonic, a perfect fifth above the 1st harmonic, and so on. If you take a slo-mo video of a rubber ball that has been hit and made to vibrate, the vibration patterns will also be a range of resonant standing waves, called "spherical harmonics".
QM predicted, through calculations (Schroedinger's equation etc) that if electrons behave as waves, they will only take up arrangements in the atom corresponding to spherical harmonics and will have different energies accordingly (lowest energy level being level 1, "the fundamental", if you like):
Level 1: one possibility - spherically symmetric mode of resonance (called "s")
Level 2: 4 possibilities - one spherically symmetrical like Level 1 plus 3 dumbbell shaped modes of resonance, at right angles to one another (in x, y, and z directions if you like) called ("p")
Level 3: 9 possibilities - one spherical (s) , 3 dumbbells (p) as above and 5 double-dumbbells, called ("d").
Level 4: 14 possibilities - 1 s; 3 p; 5d and 7 quadruple dumbbell shapes called "f".
...etc.
You will know that according to the standard atomic model, as you go across and down the Periodic Table, you have increasing numbers of +ve charged protons in the nucleus, and correspondingly more and more electrons.
According to QM, these will go into these various levels, 2 to a level, filling the lowest energy ones first. (This is something called the "Aufbau Principle".)
In alkali metals - according to this model - the common feature is you have filled up all the lower levels and have just started the next level up in energy, with one electron in that level. The +ve charge on the nucleus is the lowest it can be to start filling that level. Now, the electrostatic binding force on the electron will depend on the charge: the greater the charge, the stronger the force. So this last electron is predicted to be weakly bound - and easily lost. And this is what we find.
In the inert gases you have just filled a level completely. The +ve charge in the nucleus is the maximum it can be before you are forced to start putting electrons in the next level up. This mean the electrons are predicted to be as strongly bound as they can be, leading to low tendency to react. And this is what we find.
And the block on the left is where you are filling the "s" modes, the block on the right is where you are filing the "p" modes, the block of 10 in the middle is where you are filling the "d" modes, and so on.
So, at a stroke, QM brought a beautifully elegant explanation for the layout of the table and why the distinctive properties of each element are the way they are. The whole of inorganic chemistry relies on this QM understanding.
Now, you can do quite a bit of practical chemistry without understanding this model, as people did in the c.19th at Mendeleev's time. But it would be a bit perverse to ignore or dismiss the theory that explains the pattern so well.
