Haeckel’s recapitulation theory was long ago discounted by secular science, he made up a. lot of his claims and misrepresented embryo pictures - yet his disproven theory still finds its way into school textbooks.
Mammalian “gill slits” are folds in the region of the tiny embryo’s throat. By the 28th day of life, the embryo’s brain and spinal cord seem to be racing ahead of the rest of the body in growth. Therefore, for a time, the spinal cord is actually longer than the body, forcing the body to curl and flexing the neck area forward. (This curled embryo with the long spinal cord is mistakenly accused by some people of having an animal’s tail.) Just as many people develop a double chin when bending the neck forward, so the embryo has folds in its neck area due to this flexing.
Gill slits, thus, is a misleading name, since these folds are neither gills nor slits. Another popular name, branchial arches, is just as deceptive because branchial comes from the Greek word for “gills.” Somehow the name neck folds just isn’t fancy enough for our scientific minds, so these folds are called pharyngeal arches, since they are arch-shaped folds near the throat. (Pharyngeal is the scientific word for things having to do with the throat. When you say you have a sore throat, your doctor says you have pharyngitis.) The creases between the folds are called pharyngeal clefts, and the undersides of the folds are called pharyngeal pouches. The pouches and clefts are not connected by an opening. Each fold shapes itself into specific structures, none of which are ever used for breathing. The outer and middle ear as well as the bones, muscles, nerves, and glands of the jaw and neck and even the immune system’s thymus gland develop from these folds as tissues differentiate in compliance with the blueprint in human DNA.
Nevertheless, the terms gill slits and gill-like structures persist.
But mammalian pharyngeal arches are no more related to gills — ancestrally or otherwise — than stars are to streetlights.