Why do we have special rules for the slaughter of animals,and why do these not apply to fish?
The Torah tells us "slaughter your cattle and sheep ... as I have
commanded you" (Devarim 12:21). We don't find any directions about how to slaughter in the Written Torah, but the subject is dealt with
extensively in the Oral Torah. (In fact, this verse is one of the clear indications that an Oral Torah was given along with the Written Torah.) But we see elsewhere in the Torah that fish don't require slaughter. When Ha-Shem told Moses that he would give the complaining
people meat to eat for a month, Moses protested "Could sheep
and cattle be slaughtered for them and suffice for them? Could
all the fish in the sea be gathered for them and suffice for them?"
The Rabbis in the Talmud (Chulin 27b) explain that an animal, which was created from the ground, requires slaughtering to disconnect it from the "physicality" of life; specifically, we must sever its windpipe and esophagus. A fish, which was created from water, requires no slaughtering at all. For a bird, which was created from mud (earth and water), we require that only one pipe be severed.