A question about necessity in the Gemara

 
When the Gemara cites a necessity to explain two cases in which the principle guiding their ruling is duplicated, do both sides of the necessity have to exist?
For example: Let us assume that the Mishnah was formulated: One must set aside a tithe from the pear, one must set aside a tithe from the apple . The principle that is repeated here (all of this is an assumption) is that one must set aside a tithe from the fruits. It would be understood according to the rule we presented above if the Gemara had explained that the two fruits are different, and that they include in their characteristics a different halachic definition, which does not imply – in this case – that an apple has a halachic definition X, which does not exist in a pear , and that a pear has a halachic definition Y, which does not exist in an apple , and those halachic definitions (X and Y) would lead us to think that the apple and the pear are exempt from tithe, and therefore the Mishnah came to teach that fruits that are included in definition X are also obligated to tithe, and fruits that are included in definition Y are also obligated to tithe.
I asked – Is it correct to say that the rule I tried to present and demonstrate is not binding? I will give an example of what I mean – the Mishnah in Tractate Sanhedrin, chapter three (cited in the Babylonian Talmud, Sanhedrin 24:), mentions ‘ those who release pigeons ‘ as a type of person who performs an action that disqualifies them from testifying. The Gemara (ibid., 25-25:) attempts to clarify the concept of ‘those who release pigeons ‘. One of the opinions explains the concept as a type of gambling game, a competition between pigeons in which the winner is the one whose pigeon reaches the target first [a game that is still common today, especially in East Asia]. And the Gemara raises the question, after all, earlier in our Mishnah we discussed ‘ the game of the kobia ‘, and why are we both two identical disqualifiers in the same Mishnah? – Then it presents a necessity for both rulings, it assumes that the ‘ those who release pigeons ‘ depends on his own opinion and the ‘ those who release pigeons ‘ depends on the opinion of his pigeon (as the Gemara says):
(All of this is written in a paternalistic style so that there is no dwelling on an example that is not the main point)
“If Tana were to rely on his own knowledge, he would not be complete and would not say, “I have a knowledge of the mind, but I rely on the knowledge of the mind, not the mind.” And if Tana were to rely on the knowledge of the mind, saying, “I have a knowledge of the mind, and I know that I have a knowledge of the mind, but I rely on my own knowledge, not the mind.””
In short, in each of the cases (depends on one’s own opinion and depends on the opinion of his enemy) I had the idea that the person does not fully acquire knowledge from his own mind, because he thinks that there is a factor that is dependent on him that can, in his opinion, ensure his victory, and therefore the Mishnah changed both, so that I know that in both cases they are invalid for testimony. But here the question arises for the observer: The Gemara assumes that it was not possible to change only the first or second case, because in each case I was different, I would think and project on the second case, which is random, and therefore there is a culmination of knowledge in acquiring knowledge, and therefore that person is not invalid for testimony. But the two thoughts of the ‘God’ cannot exist together – if I think that inDepends on Juno’s opinion. There is no point in buying, in my opinion.Depends on one’s own opinion. There is a sense of accomplishment in ownership, and vice versa.
All of this is in contrast to the example we gave about the apple and the pear , where the assumption that an apple meets a halachic definition X does not contradict at all the thought that a pear does or does not meet a halachic definition Y. In short, there are necessities whose study of the first case is not related to the second case ( the apple and the pear ), and there are those that teach one thing and its opposite ( the apple and the pear ) – if I were to stand from the perspective of the first case, I would think that the second does not meet and vice versa.
I would love to know what the rabbi thinks, whether this is a correct diagnosis, or a diagnosis of nonsense, or somewhere in between.