Why are fungi and algae microbes?
Because both of those produce single-cells able to viably survive and grow on your own. For example, take a fungal spore and it can grow into a full fungus given enough food. I assume algae cells are the same way. In a single-cell form, fungi and algae qualify as self-sufficient microbes.

Animal cells are typically specialized and dependent on a support framework. Usually, a single animal cell left out on its own is largely doomed.