When something is free, people abuse it and take it for granted. This would happen to the health system if it was free at the point of use.
In countries where healthcare is free, people go to the doctors with trivial issues, miss appointments and take abuse the free service. This is a waste of resources and a drain on the public coffers.
The alternative is far worse. When people have to pay for something, they don't use it unless they absolutely have to. When it comes to health, this leads to higher death rates from preventable illnesses and worse health outcomes. In fact, health care is the field where triage was invented. An important principle of health care is to assess how to assign limited resources to those who need them most; people abusing the system will simply have to wait until resources are freed.
[P1] When something is free people abuse it. [P2] Therefore, the public would abuse a free healthcare system. [P3] This would lead to massive financial waste. [P4] Therefore, people should have to pay for healthcare.
Rejecting the premises
[Rejecting P1] The alternative is far worse.