The phrase "to promote the breed" means to support and advocate for a particular kind of animal, typically by raising awareness, encouraging adoption, and showcasing its positive characteristics. Full definition
It encourages and promotes breeding of purebred dogs whose functional health and physical features meet the standard set for each breed. (schnauzers-rule.com)
The queen promoted the breed during the second half of the 19th century. (cuteness.com)
As long as we are killing dogs and cats o = in shelters, we should not be breeding dogs or promoting the breeding of dogs. (onegreenplanet.org)