All economics problem of choice but all problems of choice are not economic problem?

Very good observation. Yes, all economic problems are choice problems but all choice problems are not economic problems. Well said. Often, however the methods to solve economic problems of choice can be applied to solve the problems of choice that are not economics. So long as there is a desirable objective function, there are costraints and there are relations among objects and constraints, many problems that are not economic can be converted into an economic-like choice problem. I hope you are aware of Arrow's book on Social Choice... Individual Values. Atsome level economic choice problems lead economists to higher level philosophy and deal with social problems which are not merely economic problems.
Love that play on words and it is so true

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