Question about Harry Potter plothole?

But remember that the Horcrux is a piece of Voldemort's soul. While in the other Horcruxes, his soul is put into an inanimate object, therefore being the only live substance in it, and can be directly stabbed, when it's in an actual person, it's protected by the other person's soul and other life parts.

Fawkes came to Harry's rescue and shed tears so quick that the venom did not have the time to reach vital organs and kill the boy. Basilisc poison is lethal enough to kill a human body before it can even kill the soul.

Hmm, good question. Maybe it's not Harry himself who'd the Horcrux, but his scar?...and the basilisk fang needed to have come in contact with the scar either directly or by the poison being eventually dispersed through Harry's body or having Harry die?...I don't know...

Though if that was the case and knowing that the poison did not kill immediately, Dumbledore should have gotten some phoenix tears ready, collected a fang, summoned Harry and destroyed the Horcrux in Harry himself