According to PHB p.82 the Oath itself is a source of power for paladins (emphasis mine).
Whatever their origin and their mission, paladins are united by their oaths to stand against the forces of evil. Whether sworn before a god’s altar and the witness of a priest, in a sacred glade before nature spirits and fey beings, or in a moment of desperation and grief with the dead as the only witness, a paladin’s oath is a powerful bond. It is a source of power that turns a devout warrior into a blessed champion.
The same is stated in Magic section on page 205:
The spells of clerics, druids, paladins, and rangers are called divine magic. These spellcasters’ access to the Weave is mediated by divine power — gods, the divine forces of nature, or the sacred weight of a paladin’s oath.
According to other answers here there is no direct requirement for a paladin to have a god or any deity that can oversee the fulfillment of the Oath: Are paladins required to follow a god?
More than that, an Oathbreaker can, in fact, deliberately deny the authority of any Oath or god over their fate and still use magical abilities: What is the source of the powers of an oathbreaker?
That being said, we can create a completely valid Paladin character without making them following any god whatsoever, because Oath itself (or "anti-Oath" in case of Oathbreaker) can serve as a source of superpowers. So, the question is, why can't absolutely any kind of strict code provide divine or magical abilities to its follower, effectively making them a Paladin of sorts? Why does it have to be a VERY specific set of rules that "triggers" magic to reveal itself within this character? What entity in DnD universe has control over exact wording of the tenets and decides, which ones are the real ones, and which ones are just a random set of ideals with no underlying sacred power?
Example: a lawful evil person can swear to themselves they would stick to a clearly stated path and ideals in order to achieve "the ultimate bad evil" or whatnot. They may have a very strict code in their evil guild that might as well serve as tenets and an Oath. Yet for some weird reason it doesn't work.
Clarification: it is clear that a set of Oaths is not a bounded set and can be expanded by DM or even WotC official extensions. This is totally fine and is, in fact, irrelevant to the question. The premise of the question is not that "there are X rules from PHB that works, why other don't?". The question is more general: "considering that not ALL oaths in DnD universe work, who decides which ones do?". I think it's quite obvious that not all oaths grant paladin powers and there are many guilds and orders in DnD universe that have 'non-working' codes, otherwise all their devout members would've gained at least a tiny fraction of paladin powers.