Continuing to think about this, and about both your reactions. It’s sort of similar to The Lobster in form, the more I do.
SPOILERS
In The Lobster, romantic interactions between people are reduced to hilariously simple schematics. The subtext of what people communicate is made text, to comedic effect (“we’re compatible because we find each other physically attractive, but we’re not too attractive to be out of each other’s leagues because we also have similar physical weaknesses…getting nosebleeds”). In the second half, those schematics are eschewed for a dramatization of what occurs when people who can’t find a compatible partner escape the compound.
Most times I’ve rewatched the The Lobster, I enjoy the first half more than the second, maybe just because it’s funny, but also because it’s really interesting to me how Yorgos communicates the obvious in non-obvious terms. Or maybe makes the so-obvious-it’s-invisible even more obvious, through them. I think he’s doing something similar, here, but to terrifying effect, on a more subconscious kick-you-in-the-gut level, and that the lack of a really big turn in Sacred Deer's third act is for thematically sound reasons.
In The Killing of a Sacred Deer, the familial damage that occurs as a result of Dr. Murphy’s alcoholism, and of his denial of his alcoholism, is transmuted into allergorical, supernatural happenings the same way The Lobster transmutes romantic interactions into simple schematics, and Dr. Murphy is brought to some awareness of the suffering he's causing his family by way of his interactions with Martin. It’s a partial journey from darkness up into light.
This movie has a similar ticking time bomb as The Lobster (30 days until you’re turned into an animal / soon you’ll be paralyzed), but the dramatic evolution that occurs towards the end of The Lobster isn’t there because Sacred Deer has a far more tragic end. In the former, Colin Farrell manages to escape his fate — it’s why the thriller-like third act in the forest exists — whereas here, Dr. Murphy's hubris and denial perpetuates. He knows Martin is a problem, but never recognizes why. His blaming and scapegoating persists ("An anesthesiologist can kill a patient, but a surgeon never does..."), so the lack of plot progression works, in my view. Ironically, in kidnapping Martin, Dr. Murphy is going after the symptom, not cause, of ailment, betraying the medical prowess he insists he has.