The Overlord wrote:
I will give no deadly medicine to any one if asked, nor suggest any such counsel; and similarly I will not give a woman a pessary to cause an abortion.
Lovely nonsense, if you want an abortion or get euthanized you are screwed. No doctor today cares about this ancient oath anymore and a fictional alien doctor in an interspecies exchange program certainly doesn't either. Archer chose a Denobulan doctor precisely because he wanted somebody with a different perspective. Gee, that's why humankind is going out there in the first place, to learn from and about other people.
You do realize the modern Hippocratic Oath is different from ancient one, right? Most doctors still respect the modern oath.
Also just because Phlox's perspective is different doesn't make it good. Phlox seems to using eugenics to justify his perspective, that a weaker race is holding a stronger race back and if the weaker race dies the stronger race will thrive. That sounds familiar.
Frankly if Phlox can just ignore the Hippocratic oath at his whim, he is not fit to be a doctor in Star Fleet. Do you think Picard shouldn't have punished Worf for killing Duras, even according to Klingon culture what Worf did was okay?
I don't believe in complete cultural relativity, that is dangerous for a society. If someone believes they have the right to beat their wife, I don't think they should be legally allowed to do that.
Why do you keep bringing up Starfleet, and what Picard would do, and the Prime Directive, none of these things exist, and Phlox is not a member of Archer's Organization that gives him his orders. He is a Cultural Exchange participant, who Archer invited along for the ride requesting he serve as the ship's Doctor, no different than T'Pol's situation as an Observer
Because he is working on a Star Fleet ship and thus is subject to Star Fleet rules and regulations. If someone is visiting another country and they break the laws of that country, trying to argue that the illegal act in question is okay in their culture would not save them from legal punishment.