The Mishna says that one who davens asking for mercy because על קן צפור יגיע רחמיך, we shut him up. The gemara offers 2 approaches as to why this is inappropriate. 1. It causes jealousy between the animals. 2. It turn the middos of Hashem into acts of compassion when in truth they are gezeiros.
The first approach seems to assume that in truth, this mitzvah is a mitzvah to have compassion on birds. The halacha in the mishna is just that one shouldn't use this in davening because to verbalize it in a way that singles out birds from other animals will cause "jealousy" between Hashem creatures. This is what Rashi seems to say - לומר על אלה חס ולא על שאר הבריות. One shouldn't say in their tefillah that Hashem only has compassion on birds. According to this approach, the halacha if משתקין אותו is only because it is being used in tefillah, but not that it is actually wrong.
Rashi explains the second approach of the gemara to be that we have to view ALL the mitzvos of Hashem as gezeiros that we do whether we understand or don't understand. The moment we start giving rationale for mitzvos, it may lead one to discriminate between what they consider more rationale and less rationale, which is obviously wrong. According to this approach, which also seems to be the approach of the Rambam, mitzvos cannot be considered acts of compassion, rather decrees of Hashem that we fulfill simply because we are his servants.
However, the Raman (ki seitzei) elaborates and disagrees. The Ramban explains that the point of this mishna and other midrashim is to say that we shouldn't reduce Hashem's mitzvos to being minor acts of compassion on birds and animals. True, the nature of this mitzvah and many others is compassion, but it is not to display compassion on the birds, rather it is to teach us to be compassionate people. Hashem wants these mitzvos to be used to be מצרף the human beings and turn them into compassionate people rather than a display of compassion on the birds.
R. Akiva Eiger in the gilyon ha'shas points to a midrash rabba at the beginning of ki seitzei that seems to disagree. It seems to consider the mitzvah of mila a form of compassion on the child and the mitzvah of sending away the mother a form of compassion on the birds. This seems to contradict our mishna? One of the commentaries on the midrash (pirush maharzu) explains that compassion on the birds is certainly one element or aspect in this mitzvah, but we cannot limit the entire mitzvah to just a mere act of compassion.