So in both the books and movies, the basilisk in the Chamber of Secrets is said to only listen to the Heir of Slytherin. We all know Tom Riddle was the Heir, but I want to know why the basilisk could only listen to the Heir? And if it is possible to get an animal to listen to you like that, is it possible that all the heirs to each house have a certain animal that only they can talk to as well?
Only Parselmouths can control a basilisk, and the Heir was one.
Fantastic Beasts and Where to Find Them explains that only Parselmouths can control a basilisk.
“However, since Basilisks are uncontrollable except by Parselmouths, they are as dangerous to most Dark wizards as to anybody else, and there have been no recorded sightings of Basilisks in Britain for at least four hundred years.”
- Fantastic Beasts and Where to Find Them (textbook)
Salazar Slytherin was a Parselmouth, and most likely presumed his descendants would be as well. It may be, though, that the basilisk was controllable by any Parselmouth, but that Salazar presumed any Parselmouth who attended Hogwarts and found the Chamber of Secrets would be his descendant. However, Harry was able to understand the basilisk as well, and he could open the Chamber.
“Ron,’ he breathed, ‘this is it. This is the answer. The monster in the Chamber’s a Basilisk – a giant serpent! That’s why I’ve been hearing that voice all over the place, and nobody else has heard it. It’s because I understand Parseltongue …”
- Harry Potter and the Chamber of Secrets, Chapter 11 (The Duelling Club)
Harry never attempted to control the basilisk, so it’s unclear if he’d be able to do it. He did have a part of the Dark Lord’s soul in him but he himself wasn’t a direct descendant of Salazar Slytherin. In fact, while he never attempted to control the basilisk either, Ron was able to open the Chamber by imitating the word in Parseltongue that Harry had used. Therefore, it seems to be based on ability to speak Parseltongue rather than heritage.
We don’t know if he was the only one who could - Harry didn’t try.
Tom Riddle was the only one who we know could control the basilisk, because he’s the only one who we saw try to control the basilisk. Harry (the only other known Parselmouth who was at Hogwarts at that time) never tried, so we have no way of knowing if a Parselmouth who wasn’t a direct descendant of Salazar Slytherin would be able to control the basilisk as well.