Why does health care face the question of rationing at all?

Because limited resources meet unlimited needs: an ageing population and medical innovation (which is both the goal and a cause of rising costs) keep pushing spending up, while the claim on health care has grown from basic "repair medicine" to maximising quality of life.

The tension, following Noll and Wolf (2017), who write about Germany:

• Limited resources vs. unlimited needs. There is always more medicine that could be done than money to do it.
• Demographics make it worse: more older people with more chronic illness.
• Innovation is both a goal and a cause: every new therapy is progress, and also a new expense.
• The claim has grown. In the 1950s and 60s the aim was an elementary level of care (Reparaturmedizin, repair medicine). Today the aim is the highest possible level of capabilities (Verwirklichungschancen), i.e. maximising quality of life. That aim has no natural upper bound, so the health system needs a socially accepted, normatively defined framework within which it operates.
• Efficiency doubts: Germany combines high spending, average outcomes and partial gaps in care (e.g. "bloody discharges", patients released too early) despite generous capacity.

This is why the question "should resources be rationed to distribute them fairly?" cannot be avoided, only answered openly or covertly.

Go deeper:

• Noll & Wolf (2017): Rationalisierung und Rationierung im Gesundheitswesen aus ethischer Perspektive — the article this unit follows (German).
• Wikipedia: Health care rationing — rationing in different health systems.