It is, of course, not just mammals, but nearly all animal life is symmetric. Even plants are usually symmetric in some degree. There are exceptions here and there. For example, one interesting exception is that of the fiddler crab which has one claw larger than another. In general, when a single appendage is present on an animal it is nearly always on the center line of the animal. For example, the horn of a rhinocerous or the central horn on a triceratops, or a human's nose.
The symmetry is generally enforced genetically, not environmentally. For example, if you hold a paper up to your face you will find that the left side of the face is different than the right side, or at least that is the way it is for most people. Thus, once conceived, the two sides of the face grow differently, a phenomena that geneticists call genetic "expression". For example, your fingerprints are "expressed" traits, not genetic traits, and for this reason the fingerprint on your left thumb is different than the fingerprint on your right thumb.
Even genetically, however, many parts of the body are not symmetric. For example, the heart is on the left side of the body, but the liver is on the right.
The evolutionary logic for symmetry probably is because it makes locomotion easier and more effective. If an animal is not symmetric, they may have difficulty moving efficiently.