If neutered early, male cats rarely develop this habit. When your female dog or cat goes into heat, the males for blocks around will know it. Walking her will be like combat. Every male dog in the neighborhood will follow, and nothing will drive them away. Your dog will normally come into heat twice a year, and she'll attract males for almost three weeks.
Cats are incredibly efficient reproducers.
They also can go into heat while nursing their current litter. Cats needing to mate will wail, rub, and dart out the door at the slightest opportunity. They become almost magical in their ability to escape. If you don't want your pet to breed, you're in for a very trying time. You'll get no cooperation from your pets because all their instincts are compelling them to find a mate.