When the Red Skull tells Natascha and Clint they must sacrifice what they love the most for the Soul Stone, they both try to commit suicide. How does that work? Do they both love their self more than anything? Doesn't seem that way. And if one can sacrifice one's self for the Soul Stone, why didn't Thanos let Gamora kill herself with that knife in Infinity War? It would have been much easier on him than to have to throw her off the cliff.
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It's admittedly arbitrary, but we're told the soul stone has "a certain wisdom"
It knows that Thanos loved Gamora and that Clint and Natasha loved each other.
And remember, Red Skull said the sacrifice meant "you must LOSE [not kill] that which you love ... a soul for a soul [so you can't sacrifice your favorite car]." He also said, "what you seek lies before you, as does what you fear."
So seems that you must lose a loved one to the cliff. Had Gamora killed herself before Thanos could chuck her over the edge, no soul stone. Whereas even where Clint or Nat threw themselves off, a loved one was "lost" and the soul stone was earned.
Oh and it's clear by this point in the film that neither of them love themselves particularly much. Clint feels he's become a monster unworthy of his family. Nat still has "red on her ledger."