A Rather Useless Inheritance
Being a Parselmouth came with the inherent predisposition to understand snake behaviours and imitate them. It was relieving Harry wasn’t going to kill anyone with venom, nor petrify them with his gaze. But also, somewhat frustrating as it was all completely useless. None of the skills that came with being a Parselmouth would help Harry survive Voldemort.
It might, in fact, have the opposite effect. For all Riddle's fury that Harry was the cause of his elder self’s defeat, he was fascinated by the fact Harry was also a Parselmouth. He had grabbed Harry’s face, turning him side to side looking bemusedly enraptured by Harry’s threat display. “At your age, I was imitating much more vicious snakes than this, Harry.”
That may have been all well and good, but Harry didn’t feel very vicious. He felt very threatened and in over his head.