Why does an orbital can accommodate two electrons only?

Why does an s-orbital accommodate two electrons only?
The Exclusion Principle only allows two electrons in an orbital.
A wave must have a crest and a trough per period. An electron in ground state, like hydrogen 1s state has a wave with no nodes, thus to be a wave, the period must have two cycles. A stationary wave must have quantized action and the node & antinode must be stationary. If we pair electrons, we double its frequency but we get a node and antinode in a one-cycle period provided motion applied by the two waves are contrary. This contrary wave motion implies that electron pairs are not going anywhere as a pair. If you add a third electron, frequency triples but now you cannot get stationary wave as nodes and antinodes move. Thus, stationary states have one or two electrons only. This has nothing to do with spin.
The reason why nodes & antinodes not moving are stable is that this situation alone permits electron motion to be in accord with Maxwell’s requirement. In that theory, wave and particle interact only at antinode and hence this position alone does not accelerate.
Let us start with a simple way of showing arrangement of electrons around an atom. Here, electrons are arranged in energy levels or shells around nucleus of an atom. Electrons that are in first energy level are closest to nucleus and will have lowest energy. Electrons further away from nucleus will have higher energy. An atom’s electron shell can accommodate 2n^2 electrons, where n is energy level. For example, first shell can accommodate 2*(1)^2 or 2 electrons. Second shell can accommodate 2*(2)^2 = 8 electrons.
As an example, fluorine (F), has atomic number of 9, meaning that a neutral fluorine atom has 9 electrons. First 2 electrons are found in first energy level and other 7 are found in second energy level.
Atomic Orbitals:
Though electrons can be represented by circling nucleus in rings, in reality, electrons move along paths which are more complicated. These paths are called atomic orbitals or subshells. There are many different orbital shapes – s,p,d and f. First energy level contains only one ‘s’ orbital, second energy level contains one ‘s’ orbital and 3 ‘p’ orbitals and third energy level cone ‘s’ orbital, three p orbitals and 5 d orbitals. Within each energy level, s orbital is at a lower energy than p orbitals.
An orbital diagram helps to determine electron configuration of an element. An element’s electron configuration is the arrangement of electrons in shells. Guidelines for working out this configuration:
Each orbital can hold only two electrons. Electrons which occur together in an orbital are called an electron pair.
An electron will always try to enter orbital with lowest energy.
An electron can occupy an orbital on its own but it would rather occupy a lower-energy orbital with another electron before occupying a higher-energy orbital.
The s-subshell can hold 2 electrons
The p-subshell can hold 6 electrons.
Electron configurations can be used to rationalize chemical properties in both inorganic & organic chemistry.