The Vulcans gave us the answer already.
Lastly and finally, it simply doesn’t make sense, logically speaking. For Tuvix to live, two must die. For Neelix and Tuvok to live, one must die. If you’re going to come on a Star Trek website and look for a debate that doesn’t include logic, you have already lost. You can’t go against logic in Trek. It will never work. Spock ended this debate decades ago.
"Logic clearly dictates that the needs of the many outweigh the needs of the few."
With Tuvix, children lose their father, women lose their spouses, a ship loses their security and morale officers, their logical rutter, and their emotional pat on the shoulder. Too many people are negatively affected by Tuvix’s creation. Ergo, Tuvix cannot exist if the needs of the many are to be placed first and foremost.
The ship wanted Neelix and Tuvok back, not a half measure that replaces them.
Some will say the Doctor was clearly on Tuvix’s side as he declined to do the procedure but one could argue that he wasn’t. Not really. While the Doctor may come across as supporting Tuvix, at this point in the series he’s still very much a basic EMH doctor, meaning he can’t operate on anyone without their consent except for life-saving surgery. So that doesn’t mean the EMH agrees, it means his programming dictates that he needs consent. It’s like saying a robot designed with Asimov’s Three Laws is a pacifist just because they didn’t strike you.
No, it’s merely their programming.
Logically, Tuvix’s existence left too many negative situations to plan for. He was not someone who could be relied on, because you didn’t know who he was eventually going to end up becoming. He reduced the crew compliment by one, and in doing so took out the two polar opposites of the ship which helped stabilize and balance things. Tuvix had no track record, while Neelix and Tuvok had a glowing one. Janeway did what she needed to do to ensure that she saved two of her crew members and the ship as a whole.
She did the logical thing, which in this case, was also the right thing to do. It doesn’t mean she didn’t take it hard, it wasn’t supposed to be an easy decision. That’s what makes it such a compelling episode even all these years later.