Bringing a pet into combat can be desirable, if it is strong enough it can give you a combination bonus and can more easily survive the fight.
*Note that if you tame your mount, creatures you fight can and will often will target your mount instead of you.
If a pet is hit in combat, it will lose loyalty. Stronger animals lose more loyalty when hit than weaker animals. If it takes enough hits without dying it can go untame. This cannot be achieved with archery however; it must be a melee weapon. As a result, when entering combat with a pet, it's helpful to assure that the pet has the highest loyalty level you can achieve.