Question

Hello and blessings,
A bit hard for me to formulate my question, and I hope it will be understandable, so I’ll use an example.
The Talmud in Bava Kamma (26a) tries to derive, by an a fortiori inference, liability for ransom payment in the case of a person who is liable for the four types of damages, from an ox, which is not liable for the four types of damages. Immediately afterward it tries to derive, by an a fortiori inference, liability for the four types of damages in the case of an animal (which does pay ransom) from a person, who does not pay ransom.
We seem to encounter here a situation in which one can go in two completely opposite directions, and both are logically valid. How can that be? Am I mistaken, and these two lines of reasoning do not actually contradict one another? After all, each one assumes that the feature possessed by one side gives it an advantage over the other.
Also, one cannot argue that both perspectives are correct and that the matter is being examined from different angles, since it is obvious (from logic, and I think I saw a source for this) that the thing we are trying to derive by an a fortiori inference conceptually belongs also to that from which we are building the inference. [It would make no sense to say: if I have a hat and you do not, then all the more so I am more full than you are.] So it is clear that these two features are on the same plane, and in every kind of a fortiori inference we are really deciding which of them is preferable.
Should we conclude that these are indeed disputing opinions in the Talmud? Or is there room for both kinds of a fortiori inference?