Here's why:
* Gait Inheritance: The gait of a horse (trotting or pacing) is primarily determined by its genetics. Trotting and pacing are considered distinct gaits with different genetic underpinnings. Breeding a trotter to a pacer leads to a foal that inherits genes for both gaits, making it difficult to predict which gait will be dominant.
* Breed Standards: Both the Standardbred and AT&P breed registries have strict rules regarding gait inheritance. They only register foals that are sired by registered stallions and dams, and the offspring must exhibit the same gait as the parent. Since a foal from a trotting mare and a pacing stallion doesn't fit these criteria, it wouldn't be eligible for registration.
Important Note: While the foal wouldn't be eligible for registration as a Standardbred or AT&P, it could potentially be registered as a "mixed breed" or under another breed registry with less stringent gait requirements. However, this would result in the foal having less desirable marketability and potentially lower value.
In summary: Breeding a trotting mare to a pacing stallion will result in a foal that is unlikely to be a consistent trotter or pacer and therefore ineligible for registration as a Standardbred or AT&P.