Spaying a dog

It is common to say that it is permitted only by a gentile. The consideration of a future tz'aba'ach is problematic in several ways. First, it is a prevention of sorrow for an unborn creature, and therefore there is currently no obligation towards it (as in the issue of "wrongful birth." Search here on the Internet in general). Second, at the moment there is no sorrow yet, and therefore it is difficult to permit prohibitions on this basis. Third, the sterilization of this creature harms it for the sake of future creatures. Fourth, it is not clear that the descendants of the dog or bitch that we sterilize will indeed suffer. This is a general public consideration and not an individual one. Indeed, the categorical imperative instructs us that such a collective consideration is correct and certainly legitimate, even if in relation to this dog it is irrelevant. See columns 122 342, 344. It is also necessary to discuss whether this prohibition is from the perspective of the tsaba'ah (the sorrow that the action causes the tsaba'ah), and then it seems that in principle there is no prohibition in this, since today it can be done without significant suffering. And even if the prohibition is from the perspective of the sabbath in the form of "leshabbat ytsre'a," meaning to let the world develop as God planned, then here it seems that there is definitely room for leniency. Although a ta'ama dekra is not required, this is only for prohibitions that are explicitly written, and this is not the case in the tsaba'ah. Beyond all of this, there is doubt whether this prohibition is from the Torah, and regarding females it is SS. Therefore, there may be room for leniency even for a Jew, and certainly by a Gentile.