The Yerushalmi FAMOUSLY asks why one can't be yotzei with matza of חדש when he has no other matza and let the mitzva of matza override the aveirah of eating חדש. In Talmudic parlance אתי עשה וידחה לא תעשה??!!!
This question is difficult to swallow [pun intended]. When one eats less than a כזית of the חדש he is already doing an aveirah because חצי שיעור אסור מן התורה. The mitzva is not fulfilled until he eats a כזית. So it emerges that the mitzva and aveirah are happening at different times. We rule that עשה דוחה לא תעשה ONLY when they happen simultaneously??!!!
