The reason for the formation of the chemical bond is still not clear, in fact, there is no physical justification, as it was at the time of Bohr, since the formation of a chemical bond does not follow from the four fundamental interactions. Just imagine, a chemical bond "does not understand" that it can not be explained normally and quietly exists :). A full explanation of the chemical bond can only be provided by quantum mechanics (in the future), classical approaches simply do not work.
To understand this, it is necessary not to forget what L. Pauling did (L. Pauling, "The nature of the chemical bond", and the work of L. Pauling: Chem. Rev. 5, 173 (1928)), namely Pauling analyzed the interaction of the hydrogen atom and the proton in the entire range of lengths (he admitted that the hydrogen atom and H + on the approach are preserved and showed that the bond is not formed in this case (since there is no exchange interaction or resonance by Pauling)). Only one of the above-mentioned facts actually destroys the classical approach (attraction and repulsion by Coulomb) to explaining the chemical bond. There inevitably follows that the chemical bond is a quantum-mechanical effect and no other.
Imagine a system with two protons and one electron, but if it is treated as a hydrogen atom and a proton, then the bond can not form over the whole range of lengths. But, as Burrau showed, the bond in H2 + is formed (if we consider the system as two protons and one electron), and no one particularly doubts this, since H2 + exists. I particularly emphasize that there is only one electron (there is no inter-electronic repulsion, etc.).
After this fact, further discussions can not be continued, they do not make sense (especially to apply this to the explanation of two-electron bond or aromatic, this is a slightly different level of complexity). But nevertheless, it should be noted that quantum mechanics introduced the concept of "exchange interaction", which had no physical justification (since no fundamental interactions are altered in the interchange of electrons, but should, if a bond is formed) explained the chemical bond (more accurately, "disguised" chemical bond into the quantum-mechanical effect of the "exchange interaction"), by this, confirming that the chemical bond is indeed a quantum-mechanical effect.
The science of chemical bonding is only at the beginning of it's journey, and it is for today's students to make the most significant contribution to the theory of chemical bonding. And this will lead to fundamental changes in understanding both chemistry and physics. On the basis of modern concepts of quantum mechanics, chemical bond can not be explained, fundamental assumptions are needed in quantum mechanics itself ...
On the photo page from the work of L. Pauling "The application of the quantum mechanics to the structure of the Hydrogen molecule and Hydrogen molecule-ion and to related problems" Chem. Rev. 5, No. 2, p. 193, June (1928).
Benzene on the basis of the three-electron bond: