So, “half goes away in taxes” is an exaggeration, but I can totally sympathize with the feeling. Especially since the quality of healthcare is declining and the pay-as-you-go pension system is only built to benefit the current generation of pensioners.
* note that, if one is earning less than 77'000€ today or less than 84'150€ in 2027, one is prohibited to switch to a private insurance. One of the most regressive precepts of the German system.