Wikipedia
Many biologists and other academics held to the idea of blending inheritance during the 19th century, prior to the discovery of genetics. Blending inheritance was merely a widespread hypothetical model, rather than a formalized scientific theory (it was never formally presented to a scientific body, nor published in any scientific journals, nor ascribed to any specific person), in which it was thought inherited traits were determined randomly, from a range bound by the homologous traits found in the parents. The height of a person, with one short parent and one tall parent, was thought to always be of some interim value between its two parents' heights. The shortcoming to this idea was in how it required the person of interim height, in turn, to then become one of the limiting bounds (either upper or lower) for future offspring, and so on down the entire lineage. Thus, in each family, the potential for variation would tend to narrow, quite dramatically, with each generation, and, so it would go for the entire population with every trait. If blending inheritance were true, in this example, all members of a species would eventually converge upon a single value for height for all members. In short, "blending inheritance is incompatible...with obvious fact. If it were really true that variation disappeared, every generation should be more uniform than the previous one. By now, all individuals should be as indistinguishable as clones."
In addition, blending inheritance failed to explain how traits that seemingly disappeared for several generations often reasserted themselves down the line, unaltered. Blue eyes and blond hair, for example, often could disappear from a family's lineage for several generations, only to have two brown-haired, brown-eyed parents give birth to a blond, blue-eyed child. If blending inheritance were fact, this could not be possible.