🚀 go-pugleaf

There are probably several answers to this.
Firstly, it is hard to find a nice, cozy, anaerobic environment that is
large enough to fit an elephant or two. The exception is the bottom of
the ocean, particularly near hydrothermal vents, where there are large,
complex organisms that get by on an essentially anaerobic life-style;
relying on sulphur oxidation instead. But even there it is the bacteria
in their tissues that do all the hard work.
That leads to the next answer. Large organisms need a lot of energy and
anaerobic metabolism is less efficient. Aerobic metabolism has a much
greater potential for producing energy and is probably a prerequisite
for the evolution of large, complex organisms. Certainly any large
organisms with anaerobic metabolism would be slow- growing and moving
and would be quickly out competed by any aerobic forms. It has been
speculated that this did actually occur at the end of the Vendian
period just before the Cambrian explosion. It is thought that the
oxygen content of the atmosphere was starting to become respectable
about then and a whole group of large organisms seemed to vanish
overnight, although there is lots of argument about that. 
Strangely, the few remaining anaerobic environments with excellent
conditions for growth are inside larger organisms. We still retain a
slice of the anaerobic past in the way that our cells exclude oxygen
from all but a restricted set of metabolic processes. However, to be a
good anaerobic parasite you need to be small and relatively simple
(parasitic elephants were not very successful).

Dean R. Hewish
Cell biologist and Flow Cytometrist
CSIRO Division of Biomolecular Engineering
Parkville, Victoria, Australia