Being psionic is something that your character is on creation, and may or may not be part of the actual concept of the character you're trying to create.
Finding a magic sword is just something that happens to that character during play, and you can react to it however you think that your character would.
Sure. And a magic sword is something you wear on your belt, while psionics exist in your mind. A magic sword is detectable by detect magic; psionic abilities are not. You can use your magic sword to open a beer bottle, but psionics...hmm, maybe that's not a good example.
In any event, we can think of endless ways that a magic sword is not 1e psionics, but the similarity relevant to the point being made remains: they both are powerful character features that you can't choose; they are the result of random dice rolls. The 1e version of psionics is not unique in this way.
And if you don't like the magic sword example, there's randomly rolled ability scores. There's also HP. There's
Deck of Many Things.
Again, I think the difference is that WotC, and some posters, think (or once thought) that psionics works well in the same category as magic items. That is, as character boosts that you can't really plan for or control for.
Other people think it should be more like choosing your class or subclass or feats: if you want it, you should be able to choose it.
Neither opinion is right or wrong. It's a difference of opinion about the design of the game. But recognizing/acknowledging that difference may help illuminate the source(s) of disagreement.