The early Christians just based their holidays around the same time as the Pagans celebrated their holidays.

Christmas: Winter Solstice. Who wouldn't celebrate the lengthening of the days? But, the Christians wanted a holiday then, so they just decided that they'd throw the birth of Jesus at around that time.
Easter: A General Spring holiday - so much happens in Spring, it can all be celebrated! Again, the Christians probably decided that because the PAGANS had a holiday then, they had to have a holiday - and the resurrection of Jesus sounded good. ;D

Well, that's my reasoning for the holiday placements.