I have a kasha on the pshat (which I think this is what T is saying), and is the main pshat of the sugya on why you would be chayav, if you push the top animal instead of pulling the bottom animal out. The implication is that the reason is a greater chance of killing the animal if you push the top one than if you pull the bottom one away. But certainly there is a chance that it can die if you pull the animal from the bottom. The reisha gives that as an example.
So accordingly, in the seifa, when the Gemara says you are chayav if you push the animal on top - how can the Gemara mechayev you? You killing the animal is an act that is mutar. You are allowed to take the law into your hands. The question is did you kill the animal when you didn't have to? So the person who took the din into his own hands, is the muchzak, he can just taina hamotzi mechvero alav haraya. Prove to me if I used the other way of pulling the animal from the bottom, it wouldn't kill you animal? You have to prove it to me. You cannot mechayve me to pay because I chose a riskier method. I am not a vadai mazik. I am a safeik mazik. Maybe it would have died the other way as well. The burden of proof is on you.
For example, if someone is a rodef, and instead of using a small gun I use a bigger gun that has a higher chance to kill him, and I do kill him. Would that be considered murder? I don't think so. At minimum, I wouldn't be chayav misa.
So too here the animal is a rodef.
Maybe you want to say that when once you killed the animal in a risky way, the burden of proof is on you to demonstrate that you would have killed it even using the non-risker way. But look at the Mishna in Bava Kama 35a it says:
If the injured animals were two oxen, one large and the other one small, and the ones that caused the damage were also two oxen, one large and one small, and the injured party says: The large one injured the large one and the small one injured the small one, and the one liable for damage says: No; rather, the small one injured the large one, in which case, if half the value of the belligerent ox does not cover half the damage, he is not required to pay more, and the large one injured the small one; or, similarly, if one of the belligerent oxen was innocuous and one forewarned, and the injured party says: The forewarned ox injured the large one, and the innocuous ox injured the small one, and the one liable for damage says: No; rather, the innocuous ox injured the large one and the forewarned ox injured the small one; here too, the burden of proof rests upon the claimant.
Thus, we see in the case where the person was a vadai mazik on the smaller value, but a safeik mazik on the higher value, the Gemara still says that he is the muchzak and the burden of proof is on the one who is trying to get money from him. Kal v'chomer if in our case where he doesn't even have the status of a vadai mazik at all, just a safeik mazik, he would not forfeit his status as a muchzak.
Menachem Zaman, Sherman Oaks
1) I will first just make a quick comment about a side point, which is connected to Maseches Sanhedrin, not to Maseches Bava Kama. This is about using the "small gun" against the Rodef, not the big gun. This reminds me of the Gemara in Sanhedrin, beginning of 74a, where Rebbi Yonasan ben Shaul said that if the pursued person could have been saved by maiming the Rodef in one of his limbs but instead the savior killed the Rodef, the savior is killed for doing so. The Rambam (Hilchos Rotze'ach 1:13) writes that anyone who could have saved the Rodef by maiming him but did not go to this bother and instead killed the Rodef, has spilled blood and is Chayav Misah, but the Beis Din does not kill him.
Therefore, it seems that if the "small gun" could have done the job without killing him, but instead he used the big gun, he is Chayav Misah.
2) The Meiri writes that if he would have pulled out his own ox from underneath, it is not "Metzuyah," likely, that the ox on top would have been killed. According to the Meiri, the likelihood that the upper ox will die if he is pushed is considerably higher than the likelihood that he will die if the bottom ox is removed. He cannot argue "ha'Motzi me'Chaveiro Alav ha'Ra'ayah" when he possessed a way of acting without causing damage to others and instead chose a different way.
3) The Sm'a on Choshen Mishpat 383:6 writes that it is not the bottom ox that he should have removed, but rather he should have removed the top ox gently. He should not have pushed it forcefully and caused its death. Again, we see from the Sm'a that if it is possible to act in such a way that does not damage anyone, one is not allowed to take the law into one's own hands.
Kol Tuv,
Dovid Bloom
1) I will bring, bs'd, another proof that killing the top ox is not an act which is Mutar. Tosfos (28a, DH Meshaber) writes that the reason why he must remove the ox is that there is no extra trouble involved in removing the ox rather than pushing the ox. One learns an important rule from Tosfos: one is not allowed to take the law into one's hands when one can act in a different, and less damaging, way without having to go to a Tircha by adopting the alternative way.
2) There is still a point which should be understood even according to the above rule concerning the limits of "Avid Inish Dina l'Nafshei." Even though he should not have pushed the ox, but, b'Di'eved, if he did, why can he not argue that "even if I would have done it the correct way, the ox might have still died, so you have no proof that I caused any damage"? This of course is your argument, Menachem.
3) According to the Meiri I cited above, it seems that we also have a limitation on the rule of ha'Motzi me'Chaveiro Alav ha'Ra'ayah. The Meiri writes that if he would have pulled out the bottom ox, the death of the top ox would not have been "Metzuyah." For the sake of example I will make up some percentages. Let us say that there is an 80 percent chance that the top ox will die if pushed, and a 20 percent chance that it will die if the bottom ox is removed. Since there is a very significant difference between these percentages, we no longer apply the rule of ha'Motzi me'Chaveiro Alav ha'Ra'ayah.
We can express this slightly differently and say that a difference of 60 percent is a sufficient proof with which to be able to take out money from the pocket of someone who pushed the ox, in contradiction to the rule stated by Tosfos that one may not take the law into one's own hands when one has an easy alternative way. The Beis Din does not always require a 100 percent proof in order to make a person pay up.
There is still a lot to discuss on this Sugya but I will close here for the moment.
Kol Tuv,
Dovid Bloom
Here is a different approach:
1) Menachem, I posed your question to a Talmid Chacham, and he had a different way of looking at the Sugya. I started off with the assumption that one is not allowed l'Chatchilah to push the top ox. This is based on Tosfos (28a, DH Meshaber) that I cited in my previous reply, that since there is no more trouble involved in removing the ox rather than pushing it, it follows that one may not push it. My question started by admitting that I was not allowed to push the ox, but now that I did so, why can I not argue that the ox would have died even if I would not have pushed it, but rather removed the bottom ox (which is the explanation of most Mefarshim, unlike the Sm'a)?
2) The Talmid Chacham answered that when somebody damages, we look at the damage he did at the present moment and do not say that if he would not have damaged then something else would have happened to commit the loss that he incurred. For instance, if a thief stole items from a house and then an hour later a terrible fire burned down the house, we do not say that if he would not have stolen it, anyway the items would have been lost so he is exempt from paying. Instead, we look at what happened at the moment, and when he stole them they were valuable, so he must pay. (It transpires that the owner of the house is actually happy that they were stolen, because now he is repaid by the thief.)
3) The proof for this is from Bava Kama 17b, where Rava says that if someone threw a Kli off the roof and someone else came and broke the Kli on its way down with a stick, the second person is exempt because "he broke a broken vessel," since it was doomed already. However, Tosfos (DH Zarak) writes that if A threw a stone on a Kli and B broke the Kli before the stone reached it, it is obvious that B must pay. Tosfos writes that there is an obvious difference between throwing a Kli off the roof and throwing a stone towards a Kli.
4) If we apply the above Tosfos to the scenario where the top ox jumped on the bottom ox, it seems clear that the top ox is not similar to a Kli thrown off the roof. The top ox is far from doomed if one removes the bottom ox. Therefore, the person who pushed the top ox is similar to the person who broke the Kli on which a stone had been thrown before the stone arrived, where, according to Tosfos, the person who broke the Kli is Chayav to pay.
Kol Tuv,
Dovid Bloom