Why is a chicken slaughtered, but not a fish?

After much thought and research I think that the requirements for slaughter are based on the sacrificial rites. The Tractate of Talmud which deals with the laws of Shechita (ritual slaughter) is named ‘Chullin’, meaning non-sanctified, i.e. not part of the sacrificial rite. Originally, when the Jews were in the desert, all meat that was eaten would be slaughtered in the Tabernacle, and become a sacrifice (most of the meat of the sacrifices would be eaten by the person who brought them). Therefore fish, which were never offered as sacrifices, do not require slaughter. Similarly those types of locust which are Kosher don’t require ritual slaughtering (though we don’t eat them nowadays anyway according to most traditions).

Regards,
Rabbi David Sedley