You are also right about society not caring, though I would argue it's the system we subscribe to.
How is this different in the context of healthcare for women?
I'm hesitant to fully jump on board with your comment because it's close to bringing the whole 'men too' crowd which often has a note of toxicity to it.
This is irrelevant. The point is either valid or it isn't. Neither you nor the person you're talking to are responsible for the reactions of third parties. Judge the point being made on its own merits.
The argument shouldnt be men vs. women, but people vs. those who exploit us, or people vs. the problem
In an ideal world, maybe. But the health issues in question are relevant to a person's sexual development (male vs. female) therefore it is functionally impossible to remove sex from the discussion.
This is kind of incorrect. The leading cause of death (in the US) is heart disease, followed by cancer:
https://www.voronoiapp.com/healthcare/What-are-the-leading-causes-of-death-for-men-and-women-4775
Obviously those affect both men and women, but men are represented higher in both causes. Heart disease and cancer absolutely have large research groups focused on them, they aren't being ignored by society at large.