I used to believe that embryos pass through periods of development representing earlier evolutionary stages

The way you stated it is actually not wrong, especially if your use of "representing" means "looking like". What is wrong is the much stronger statement that follows, "basically a fish", as opposed to, say, "human embryos pass through a stage where they have slits in their necks resembling gills, though without the same function". I suspect that this is closer to what your father meant.