That's because you could use your same argument about any public service. We pay for it in spades through income and council taxes.
Deliberately semi-quoting your argument:
You get public services for an insanely low price (healthcare, firemen, police, libraries, schools) for your own private benefit. You are forcing everyone around you to pay for you to not die/not have your house burn down/not get robbed/learn/get your kids educated etc because you don't feel like paying for it yourself.
Can't afford your own healthcare/fireman/police/library/school? Then perhaps we shouldn't let you use them unless you are willing to pay market rate for the service.