To be born is to die.
Firstly for Tuvix to die, he would have had to been born. Not merged through an accident, but created from scratch and developed into a sentient being. Tuvix was not “his own being”, but parts of Tuvok and Neelix. Nothing about Tuvix was original, just a weird combination of parts from two other wholly unique individuals.
Just because he was different from them in some ways, does not mean he was ever uniquely born or created. He didn’t develop his own personality but was constantly clashing against two identities that could not coexist. His love for both Kess and T’Pel proves this. Neelix never met T’Pel and Tuvok had no interest in Kes. If he were a solely unique individual, he would feel nothing for either woman. Why would he? He’d be unique. He’d have no memories of anyone else’s life. He would, like all life, start from the beginning.
Tuvix never learned to read, walk, or talk. He never had to earn his place in the universe. Even the EMH doctor evolved, forming his own memories and personality. He had a creator. A person he could call father. He was unique and original in a way that redefined the idea of a soul. Beyond that, he learned to feel. To express himself. He developed into a person with a unique personality.
Tuvix was an accident in the most literal definition. There was no intent there. No one was trying to merge two beings together.
This isn’t like when people have sex and have an unplanned pregnancy. When you have sex, you accept that one of the consequences could be an unplanned pregnancy. No one ever sits down to have a slab of ribs and nine-months later spits out a baby for some reason.
Same thing for computer intelligence. It’s not too often you hear a story about a guy developing a rope and pulley system that can deliver snacks from the kitchen to the living room, only to accidentally create a learning, sentient computer program.
The Doctor didn’t just come out fully cooked. Tuvix did. There was no point of conception, no Eureka moment where the creation is finished. No intent to create life and no biological reason why it should exist in the first place. Tuvix, for all intent and purposes, was an abomination.