How is Harry still a Parselmouth?

Question

He has had this ability because he hosted a part of Voldemort's soul:

“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself onto the only living soul left in that collapsed building.
Part of Lord Voldemort lives inside Harry, and it is that which gives him the power of speech with snakes, and a connection with Lord Voldemort’s mind that he has never understood. And while that fragment of soul, unmissed by Voldemort, remains attached to and protected by Harry, Lord Voldemort cannot die.”
(Deathly Hallows, Chapter 33, The Prince's Tale)

But now that Voldemort is fully dead, there's no reason why he would still be a Parselmouth.

In fact, this is confirmed in Pottermore:

Harry can no longer speak it
Harry being an accidental Horcrux meant he was bound to Voldemort in so many ways, just like Voldemort was bound to serpents. Not only could Harry speak the language of the snake, but could see through the eyes of Nagini, another of Voldemort’s Horcruxes as it turned out.
Once the part of Voldemort’s soul that dwelled inside Harry was destroyed, however, Harry discovered he was no longer a Parselmouth; an added bonus of Voldemort’s demise.
https://www.pottermore.com/features/everything-you-didnt-know-about-parseltongue

This conclusion is also reached here and here.

So, why is he able to speak Parseltongue in the Cursed Child?

Answer 1

What I am thinking is after you learn it you don't forget it. Because even Ron was able to speak some parsel words to open the chamber of secrets passage after hearing them from Harry's sleep talking. So i think it is possible that harry would still remember all the words of that. So that he would be able to speak the language and understand it. Its just like remembering a language with only "S and Sh" s.

PS. It is just like a person doesn't forget English language even after best oblivious charm.

Answer 2

It's the same reason his scar hurts, because now somewhere in an alternate timeline, Voldemort isn't actually dead. Harry's soul-to-soul connection (the one that made him a Parselmouth) is re-established once there's a soul for his own to connect to.

Note this scene just after they use the time-turner to humiliate Cedric.

He emerges back up again. Now thoroughly panicked. He looks around.

Albus . . . ALBUS . . . ALBUS.

And there’s a whisper in Parseltongue. Which travels fast around the audience. He’s coming.

He’s coming. He’s coming.

It would appear that Pottermore oversimplified the link between Harry and Voldemort. It wasn't just that Harry had a part of Voldemort inside him, it was also that they were mentally connected that gave him his abilities.

Answer 3

Because neural connection of this language became active again. The answer to this is same as this one:

It has been addressed in Act Four, Scene Fifteen - A Beautiful Hill (The Cursed Child):

Harry: You know, I thought I'd lost him - Voldemort - I thought I'd lost him - and then my scar started hurting again and I had dreams of him and I could even speak Parseltongue again and I started to feel like I'd not changed at all - that he'd never let me go -

Albus: And had he?

Harry: The part of me that was Voldemort died a long time ago, but it wasn't enough to be physically rid of him - I had to be mentally rid of him. And that - is a lot to learn for a forty-year-old man.

So, it seems that old neural connections resurfaced again. Why did it happen exactly during this time? Well, it can be coincidence or because of fights with Albus or because of prediction of Bane (which induced certain emotions) or because of The Force prophecy.

Answer 4

I see 3 reasons why Harry still is a Parselmouth:

1. A Horcrux is Black Soul Magic. The Piece in Harry may have been small but he was with it for 16.5 years! His soul and magic probably absorbed the trait as a side effect especially as the link between Harry and Tom was strengthen by Tom trying to subvert Lily's Sacrificial Protection by taking harry's blood. Blood is said to contain a bit of the ESSENCE OF ONE'S SELF likely a small trace of the magic of one's soul. So with Lily's Protection changed and thus strengthening the link between the two that meant harry had a natural yet unconventional Horcrux in Voldemort likely about the same percentage of the soul as Harry had of Voldemort in his scar. Magic has consequence when one such as Voldemort says in Goblet of Fire " pushed the boundaries of magic, perhaps, than they have ever been pushed".
2. Delphini was not even thought of yet before the Chamber of Secrets. Harry was in Salazar Slytherin's Personal Chamber which was meant for his heir. Is it not reasonable that Salazar bound the chamber to not only a Parselmouth but the Slytherin Family Magic as a whole as a test to recognize the family heir by blood or by magic. Salazar lived in Feudal times! The Family Magic was established in Feudal times! In a place filled to the brim with Slytherin Family Magicks he for a third/thrice time in combat beat Tom Marvolo Riddle, the last descendant of the MAIN SLYTHERIN FAMILY BLOODLINE! Is it not logical then to think that Harry may have become the New Lord-Apparent of the Houses of Gaunt and or Slytherin by Magical Rite of Conquest?!
3. Muggleborns are the descendants of at least one squib and thus are at least Half-bloods. The Gaunts were very into incest to keep the bloodline "PURE" and Merope Gaunt was already rebellious against her family just like Isolt Sayre, Daughter of Rionach Gaunt. Is it truly unreasonable to think that Lily Evans was a descendant of a rebellious Gaunt or possibly a squib Slytherin before the family became the Gaunts?!