The Matchmaker

If you go under the "Pets" menu, one of the links is titled "Matchmaker". It will bring you to a page where you can type in the ID of your two pets and breed them together.
Sometimes, depending on what species are being bred, the system will automatically do the litter which can result in offspring that, more often times than not, do not or very loosely resemble the parents. The reason for the often extremely different coloring of the offspring is because of the way the automatic Matchmaker's system applies layers to the offspring. For example, a pet may be bred with another pet, imagine both are purple. Now if one parent has a green layer under their visible purple layer and the other parent has a brown layer under their top layer, then one (or more) of the babies may turn out to be brown, green, or a kinda gross looking greenish-brown.*
*More detailed/accurate information from a (preferably) recent or current breeding mod would be much appreciated.