Christmas that falls in every 25 December throughout the world is observed in winter in the northern hemisphere but in summer in the southern hemisphere.why?

Because the northern and southern hemispheres have their seasons at opposite times of the year, and Christmas is not a celebration of a season.

Christmas celebrates the birth of Christ, and like most birthdays, it stays on the same date no matter where you go in the world. So in Australia, Christmas is 25 December, which happens to be in summer time. And in Europe Christmas is also on 25 December, which happens to be in winter. If you don’t know why the seasons are different in the two hemispheres then you need to read up about the Earth’s axis tilt: Axial tilt - Wikipedia

The season — winter or summer — is not a core part of the Christmas celebration. Bethlehem did not have reindeer and sleighs when Christ was born.

We don’t celebrate Christmas in a season, we celebrate it on a date. And because the whole world does not experience the same season at the same time, Christmas will be different in the tropics, the polar regions, the northern temperate zone, and the southern temperate zone. But it will always be 25 December.