Why German and other European countries use tiled roofs instead of concrete roofs as we have in Asian countries?

The need sturdier buildings to withstand all the elements and the more erratic climate, plus they use the roofs for multiple purposes. In Europe, the bigger buildings have concrete roofs as well, just like in Asian countries.   

Roof would collapse (snow).

Because it's easier to carry one tile after another than to lift several hundred kilos of concrete in one go

Also, the recipe for concrete was lost for several centuries. The Romans made concrete, mediaeval people did not

Because Europeans aren't Asian.

Builders built with whatever was cheap and to hand and importantly what suits the climate. If you don't get a lot of snow, pitched roofs are not essential as you don't need it to slide off.