you will need to euthanise something, unless you go strictly public health.
While there are public health roles that wouldn't require this, there are also public health roles that do require euthanasia. In fact, what they could require would be culling. Which could be either better or worse, though I'll vote for worse. In controlling certain epidemics (epizootics), vets cull massive numbers of animals. Serious outbreaks (the two that jump to mind are FMD, AI) the numbers of animals culled can be hundreds of thousands to millions, depending upon the location and the disease. So while you don't have the emotional component of it being someone's pet, you do have the dramatically higher numbers of animal lives lost. And you also have to deal with the fact that perhaps there isn't a personal bond between human and animal, but in culling you are destroying someone's livelihood. Sometimes governments compensate for this loss, but it is often not enough to keep the farmers from ruin (especially for the smaller farmers). So that's pretty darn emotional right there.
I'm mostly aware of this type of activity for other countries, but the US is not necessarily immune. Our protections against introductions of foreign animal diseases are better than many other countries (but probably not better than the UK, and they've had FMD twice this decade, issues with bluetongue, sporadic AI outbreaks in wild birds, etc., so the US
is at risk).
Now, not every public health vet is going to end up having to cull animals. But even if you're not the one culling, public health vets who are monitoring diseases globally (surveillance, response, containment) deal with the issue of culling every single day as a fact of life. And even if you're interested in the human applications of these diseases, the zoonotic aspect means culling is still a part of your daily awareness.
Hrm...sorry, didn't mean to seem like I was ranting. Can you tell this area of vet med is my fav? But ultimately, euthanasia (in whatever form) is something that I don't think any vet in any area of the profession will be able to avoid. It's something to very seriously consider before jumping in.