We have learned above (see daf 78) that the Torah forbids the slaughter of an animal whose parent was killed on that day. Similarly, if the offspring was killed first, the parent cannot be slaughtered on that day (oto ve-et beno – see Vayikra 22:28). The Mishna on today’s daf teaches that if mother and offspring were sold on the same day, the person who made the first purchase has the right to slaughter his animal first on that day, precluding the second from slaughtering. If, however, the person who made the second purchase went ahead and slaughtered his animal first, he has successfully claimed the right to do so and the other purchaser may not slaughter the animal that he purchased that day.
The reasoning for this law is explained in the Tosefta. When someone purchases an animal, there is an implicit understanding that he is buying the animal in order to slaughter it on that day. For that reason, he has the right to slaughter the animal that he purchased before the seller slaughters the animal – the mother of the offspring – that he retained. When a second person makes the second purchase, the seller cannot offer him greater rights in the animal than he, himself owns. Therefore the second purchaser buys an animal that should not be slaughtered if the first purchaser chooses to take advantage of his right to slaughter his purchase first.
Based on this explanation the Rosh rules that the law of the Mishna applies only if the two people purchased the animals from a single supplier. If, however, they bought their animals from two different sellers, then this law would not apply, and either of them has the right to slaughter the animal that they purchased first. The Ba”h suggests that they use a lottery to decide who should go first.