Proven false in 1874 by Professor Wilhelm His, Sr. Ernst Haeckel was convicted of fraud for this in 1874. Human embryos never have gills — not even rudimentary ones. If his theory was disproved…then why is it still printed in school textbooks everywhere as fact?
A very detailed review of the positive and negative aspects of Haeckel’s work, and His’s objections, can be found here:
wwworm.biology.uh.edu/evodevo/lecture2/richardson02.pdf