OMG! That's a shallow argument considering the complexity and interdependness of the issue.
The issue with private healthcare isn't profit-making but profiteering. Not some but a large portion of private healthcare providers have been known to profiteer through unethical means.
https://en.m.wikipedia.org/wiki/Profiteering_(business)
Due to lack of time, I can't explain in detail why healthcare is a public good and should be made available to all. Private healthcare, though helpful, cannot make up for public healthcare.
I would encourage you to read more on health economics. The debate between public & private healthcare is complex and would require a broad perspective.
https://www.coursera.org/learn/health-economics-us-healthcare-systems#syllabus
My personal opinion is that quality healthcare should be made available to everyone without judging the ability to pay. No one should be bankrupt or lose his life savings because of a health emergency. And, it isn't expensive or improbable to provide healthcare to all.
Nearly every major developed country in the world (Canada, Germany, UK, France, Australia etc) has public funded healthcare. It's a model that India should aspire to follow. That's what matured, developed countries do.