How does universal healthcare in Europe work?

Different countries have different system, so the question needs over 40 answers - one for every european country
Take Sweden - you might pay more taxes as the healthcare is covered by the state. You have to know the exact amount. Find an American family with the same income, paid taxes etc. Find out how much they pay for health insurance and then compare. It might be that the Americans pay more.
Again you have to find out what a person has to pay for privatly in Sweden and USA. How much does it cost to see a dentist, how much do glasses cost.....the list is long .
#Then you can take out a privat insurance covering the things which are not covered by the state.
This you have to go thru for every single country in Europe to come up with a fair comparasing between the european countries and USA.
What your professor said is in my opinion a bit too superficial and with too little background knowledge.

Check out these links at Wikipedia to get your research started:

http://en.wikipedia.org/wiki/Universal_health_coverage_by_country

http://en.wikipedia.org/wiki/Health_systems_by_country

http://en.wikipedia.org/wiki/Universal_health_care

http://en.wikipedia.org/wiki/Single-payer_health_care