In the context of animal breeding, the incorrect statement is about option 1, which is in-breeding. In-breeding refers to the mating of animals that are more closely related within the same breed for a few generations (typically 1 to 2 generations). Through in-breeding, breeders aim to concentrate desirable traits in the offspring. However, it can also lead to an increased expression of undesirable traits or genetic defects.

Option 2, out-breeding, is correct. Out-breeding involves the mating of unrelated animals within the same breed but without any common ancestors for several generations (typically 4 to 6 generations). This helps to maintain genetic diversity within the breed and reduce the likelihood of inbreeding depression.

Option 3, cross-breeding, is also correct. Cross-breeding involves mating superior males of one breed with superior females of another breed to obtain offspring with desirable traits from both breeds. This is often done to improve the overall quality of the offspring.

Option 4, out-crossing, refers to the offspring that is a result of out-breeding or cross-breeding. It is not the correct option as it only defines the offspring and not a specific breeding technique.

In conclusion, the correct answer is option 1 because in-breeding is