Taxonomy isn't an arbitrary classification for convenience akin to call numbers in a library, but a reflection of our best understanding of evolutionary history, and as such changes as we learn more. Already in the 19th century many biologists already doubted that fungi were plants based on the fact that they don't have chloroplasts or photosynthesize and thus need to feed off of other living things as do animals. However, with the development of sequencing methods, first for proteins in the 1950s and then for DNA in the 1970s, more quantitive support for the similarity of fungi to animals were obtained. And in the 1990s when whole genome sequencing became possible yet more information supporting the grouping was obtained.