How was it actually explained in 2e that only humans could be paladins?
I found no explanation in AD&D 2ed PHB I have, but it's like asking why only dwarf could be a dwarf.
even better, why can a half elf be a fighter/druid but an elf can't?
race uniqueness was somewhat arbitrary, at least going by how bg dealt with things
Games are arbitrary by their nature. Different buffs, debuffs and limitations are reasons for experimentation. Without that you get something bland like Pathfinder. "Oh golly! Now I can make druid-mage dwarf!" quickly lost its charm.
I don't totally agree. Games are reasoned by nature. Designers decide the strengths and limitations of every aspect of their worlds, as to create an experience that rises above sandboxy make believe. Wether the game feels arbitrary or not is a factor of novelty multiplied by the quality of that reasoning.
To someone who's only known a given version of D&D then humans being the only paladins comes across as natural as a matter of fact, in the archetypical 'humans can be anything' sense or in the 'well, thats what paladins are, holy human knights'. To someone else who's familiar with a given version of a D&D setting, then there could be an in-universe reasoning for why only humans can be paladins. There's also a third reasoning that arises purely from rules design, similar to how meta-humans can multi-class while humans can dual-class. But none of these instances are actually arbitrary.