Problems classifying organisms as different species:
The extinct species greatly outnumber the living.
Most species did not leave fossils/fossils are incomplete.
If organisms only known from fossils, we can’t test if they can interbreed and produce fertile offspring.
There is considerable variation within any one species.
Groups of organisms that are isolated form each other by oceans etc may be classified as different species but can interbreed.
Ability to interbreed cannot be tested on organisms which use asexual reproduction.