Question Why would tonic water kill a tomato plant when used as its primary water source?
Answer I never tried this experiement, so I will have to guess. There are two possible explanations.
1. Tonic water is bubbly because is has carbon dioxide added to the water. The bubbles make the water acidic. Maybe tomato plants don't like acid water.
2. A much more likely answer is that the problem is from one of the other ingredients added to the water. Tonic water also contains sugar (or high fructose corn syrup), citric acid, natural and artificial flavors, and quinine. Old-fashioned tonic water had a lot of quinine in it, but modern stuff just has a few drops.
After reading the list of ingredients, I don't think any of the ingredients in the tonic water would hurt a tomato plant. I bet if you do this experiment yourself, you will probably find that the tomato plant grows just fine with just tonic water to drink.
If any of the ingredients cause a problem, it would probably be the sugar (or corn syrup), which might cause bacteria or fungus to grow in the dirt and hurt the plant.