Final answer:
Breeders did not discover that traits are governed by genes because they believed in the blending theory of inheritance, which was disproven by Gregor Mendel's experiments that showed traits are inherited as discrete units.
Step-by-step explanation:
During the time when selective breeding was practiced, breeders failed to uncover that traits are governed by discrete units of inheritance, or genes, due to the prevailing belief in the blending theory of inheritance. This theory posited that offspring displayed an intermediate mix of parental traits, a view reinforced by the observation of continuous variation in traits such as human height. However, this concept was challenged by Gregor Mendel's experiments, which showed that traits are inherited as distinct units, observable in patterns of dominant and recessive alleles among his pea plants. His work remained largely unnoticed until the early 20th century, when it was rediscovered and found to align with observations of chromosomal inheritance, leading to the modern understanding of genetic inheritance.