In the early chapters of Pokémon Special it is rare to see adults, more specifically, it is rare to see parents. Like most of the first and second generation Pokédex Holders, Blue’s parents are never seen in the series. Many of the trainers mention their parents at least once. Blue, however, never makes a note of his parents and only mentions being raised by his grandfather and sister, Daisy. He was only even raised by his blood relatives for the first few years of his life, because when he was young he left and trained under Chuck and he continued his training right up to when the series began.
This is my town! Whoever threatens it, and my grandpa, needs to deal with me first. (Page 07, Chapter 28)
What does this mean for Blue? Based on Blue’s family structure it is likely that his parents are either deceased or unfit to take care of him. Blue doesn’t have a relationship with his parents, which makes him care about his remaining family even more. Blue will do anything in his power to keep his grandfather safe and make sure nothing happens to the things he cares for.
You listen carefully, Red! I'm going to take on Team Rocket alone! Don't interfere!! (Page 06, Chapter 28)
Blue rescues his grandfather in almost every arc that he appears in and acts rashly, completely disregarding his training and his usual attitude to keep his grandfather safe. Without a doubt Professor Oak is Blue’s weakness.