The rationale is explained at Mental Floss:
In Part II of his Summa Theologica, Aquinas wrote:"Fasting was instituted by the Church in order to bridle the concupiscences of the flesh, which regard pleasures of touch in connection with food and sex. Wherefore the Church forbade those who fast to partake of those foods which both afford most pleasure to the palate, and besides are a very great incentive to lust. Such are the flesh of animals that take their rest on the earth, and of those that breathe the air and their products."Put differently, Aquinas thought fellow Catholics should abstain from eating land-locked animals because they were too darn tasty. Lent was a time for simplicity, and he suggested that everyone tone it down. It makes sense. In the 1200s, meat was a luxury. Eating something as decadent as beef was no way to celebrate a holiday centered on modesty. But Aquinas had another reason, too: He believed meat made you horny."For, since such like animals are more like man in body, they afford greater pleasure as food, and greater nourishment to the human body, so that from their consumption there results a greater surplus available for seminal matter, which when abundant becomes a great incentive to lust. Hence the Church has bidden those who fast to abstain especially from these foods."Saint Paul's first letter to the Corinthians, for one, has been used to justify [excluding fish from the meat category]. Paul wrote, " … There is one kind of flesh of men, another flesh of beasts, another of fish, and another of birds" (1 Corinthians 15:39). That distinction was possibly taken from Judaism's own dietary restrictions, which separates fleishig (which includes land-locked mammals and fowl) from pareve (which includes fish). Neither the Torah, Talmud, or New Testament clearly explains the rationale behind the divide...It's arbitrary, anyway. In the 17th century, the Bishop of Quebec ruled that beavers were fish. In Latin America, it's OK to eat capybara, as the largest living rodent is apparently also a fish on Lenten Fridays. Churchgoers around Detroit can guiltlessly munch on muskrat every Friday. And in 2010, the Archbishop of New Orleans gave alligator the thumbs up when he declared, “Alligator is considered in the fish family."
There's more at the ever-fascintaing Mental Floss link.