This is a pretty wild straw man fallacy, but I'd like to give a good faith response nonetheless.
You may not know, but the US spends more per capita on healthcare than any other country in the world, by a longshot. Many other countries provide unimpeded treatment for all of their patients. If a doctor in Japan wants chemo, the patient gets chemo, and treatment starts immediately. So how does it make sense that we spend more on our patients but doctors are still told no, the patient can't have that treatment? It's because a larger share of our biggest-in-the-world healthcare spending goes to for profit companies, like insurance companies, than anywhere in the world.
So when an insurance company says no to a treatment, it's not because we don't collectively spend enough for that treatment, we do! It's just that the insurance company wants that spending for themselves.
https://www.econtalk.org/christy-ford-chapin-on-the-evolutio...
Spoiler alert -- the author being interviewed doesn't have a solution, quick, easy or otherwise. But the history is fascinating -- in the end there are a lot fewer villians than you might imagine. A lot of good faith decisions seemingly made in the public interest over the past 150 years have led us into a weird local minimum that seems inescapable. Where we are was not inevitable, and as they say if something is unsustainable it has to end eventually, but before suggesting sweeping solutions I'd recommend hearing a detailed history.
I know for example, my grandmother who lived in europe many years ago, had failing kidneys. While today it's likely she could have subsisted for more years on dialysis, perhaps that money didn't need to be spent.
Life is finite, and racking up bills at EOL is a waste. People need to learn how let others die with grace, instead of giving chest compressions to a 85 year old 80lb grandmother.
Your interlocutor was actually using "reductio ad absurdum", which is a valid style of argumentation. https://en.wikipedia.org/wiki/Reductio_ad_absurdum
You didn't address the scenario as presented, or demonstrate how it violated a principle you had described. Instead, you shifted to excoriating the insurers for greed and waste.
Should the insurance company bankrupt itself on the first client? If not, how should they decide how much to spend on each? I should note that non-profit hospitals have similar results as for-profit hospitals (in the USA), so there's little evidence of shareholder greed playing a significant role (though there are many other stakeholders including employees).
Of course resources are finite, nobody ever argues that they're infinite. But we treat healthcare as if there's a constant scarcity of medicine with how much is charged because there's a constant urge to squeeze even more profits out of patients who probably have only 2 choices- pay for the medicine or die.
It sucks and no one likes it, but what is the alternative?
Each human life is worth infinity? So we should bankrupt the entire country, spending 10 trillion dollars on a surgery that has a 1% chance to save a 98 year olds life?
Obviously that is an extreme example.. but the point is sound. We only have so many resources, how do they get divided up? Should be spend millions to give 80 year olds 1 more year of life? Do we value life on the reverse of age, so a baby we value at 10 million dollars, but a 90 year old we value at $20,000? What if that 90 year old is your Grandpa?