This is my guess on the reason for Delgado's hind legs having been amputated: he was 2-3 kilograms underweight at birth, rendering his hind legs malformed and needing to be amputated.

  Also, Delgado's biological father (probably a famous racing dog named Dash) and Delilah might've wanted to name their puppy Dash Jr. (after the dad), but due to the baby being born underweight, Dash changed his mind for Delgado (he had a really bad sense of humor).

Alternatively, maybe Dash was disgusted by how the puppy turned out and refused to consider the puppy his own because "it would destroy [his] athletic reputation."

  Luckily, Delgado's now maintaining a much healthier weight, though it does tend to fluctuate.