The gemara in Makos has a debate how a lav ha’nitak l’aseh works: does the fulfillment of the aseh take off the punishment of malkos (kiymu v’lo kiymo) or is it the violation of the aseh which will result in incurring malkos for the lav (bitlo v’lo bitlo). Rashi in the sugya of shiluach ha’kan (Chulin 141a d”h kiymo) writes a chiddush: if you hold kiymo v’lo kiymo the aseh must be fulfilled within toch k’dei dibur of the lav. The Rambam makes no such stipulation when he quotes that halacha. Just passing on an interesting mareh makom.
The Mishna in Brachos writes that one cannot ask in tefilah that Hashem should have mercy on us like the mercy exhibited by the mitzvah of shiluch ha'kan in sending away the mother bird. The gemara explains that we must treat mitzvos as gezeiros, not something that we do for a particular reason. Yet we find in Midrash (and the Rambam writes in Moreh) that the mitzvah is in fact about being merciful and avoiding causing pain to the mother bird.
R' Soloveitchik and Rav Kook explain that there is no contradiction here. When one is learning Torah and approaching mitzvos in an intellectual way, then one can delve into taamei ha'mitzvos. However, when one is davening, one must take the approach that our job is simply to fulfill the ratzon Hashem, with no reasons, without even trying to understand. Avodas ha'lev has different parameters than avodah with the brain.
Sefas Emes (5647) offers a different answer. The mother bird can't watch its offspring taken only because Hashem planted rachmanus in mother birds when he created the world. Hashem implanted all aspects of rachmanus that exist in the world -- if he did not create nature that way, it would not exist that way. What the Mishna means to tell us is that we should not think the bird inherently feels pain when its offspring are taken and halacha and the mitzvos haTorah are a reaction to that. To the contrary, it is the mitzvos haTorah, the gezeiras Hashem, which is what defines nature.