I’m fairly sure this is never answered definitively, but I can make some guesses.
The death of his mother
Tom Riddle’s childhood was defined by death: specifically, the death of his mother. That’s how he came to be left at the orphanage. Listen to how he reacts to the news that he has magical abilities:
“My mother can’t have been magic, or she wouldn’t have died,” said Riddle, more to himself than Dumbledore.
— Half-Blood Prince, chapter 13 (The Secret Riddle)
With no knowledge of the magical world, he immediately assumes that wizards have the upper hand. Magical folk are stronger than muggles, and their power makes them immortal.
I think he saw his mother as weak for abandoning him, for succumbing to death and leaving him in an orphanage. This view was probably reinforced when he learnt the circumstances of her upbringing and his birth. (I can’t imagine Riddle was pleased to have an almost-Squib as a mother.)
This sets up the idea that death is a human weakness and frailty, and something to be bested. It also gives him a way to prove, once and for all, that he is better than his mother.
His desire to be different
We get another hint in the same passage: this time from Dumbledore.
“There he showed his contempt for anything that tied him to other people, anything that made him ordinary. Even then, he wished to be different, separate, notorious.”
— Half-Blood Prince, chapter 13 (The Secret Riddle)
Everything dies. (Well, almost everything.) There aren’t many ways to be more different than to not die. It would be the ultimate standout moment, something that would stand him apart from everyone, forever. It would assert his (self-believed) superiority over all living beings.
A desire for power
We know that Voldemort craves power over. JK Rowling has described him as a psychopath on multiple occasions, and we know that he was a bully in the orphanage. He didn’t just want to be different, he wanted to be better.
Voldemort saw death as a human weakness:
If Voldemort saw a boggart, what would it be?
Voldemort's fear is death, ignominious death. I mean, he regards death itself as ignominious. He thinks that it's a shameful human weakness, as you know. His worst fear is death, but how would a boggart show that? I'm not too sure. I did think about that because I knew you were going to ask me that.
— The Leaky Cauldron and Mugglenet interview JK Rowling, part 2 (July 2005)
So why does he think death is a weakness? Because from the perspective of the living, you can’t be any more powerless than dead. You can do nothing. Given his lust for power and influence, I think he was scared of that degree of helplessness. He would see it as unbearable to be unable to affect the world around him.
He doesn’t just fear it; he sees it as the worst possible fate. Quoting Dumbledore:
“Your failure to understand that there are things much worse than death has always been your greatest weakness—”
— Order of the Phoenix, chapter 36 (The Only One He Ever Feared)
There’s a complete dearth of any knowledge of death in Potterverse. There’s a vague notion that a soul survives after death, but in what form is unknown. I don’t think he could contemplate the prospect of being dead, and having to give up any influence on the physical world.