In a recent interview, Dragon Ball creator Akira Toriyama revealed that for Saiyans to become powerful Super Saiyans, they need to have enough S-Cells. Dragon Ball fans are already comparing this revelation to midi-chlorians.
When asked if anyone who trains enough can become a Super Saiyan, Toriyama replied (via @Herms98), “It’s not like anyone can become a Super Saiyan through training and anger. In order to become a Super Saiyan, one’s body must contain something called ‘S-Cells.’”
Toriyama explained that once these S-Cells reach a certain amount, anger can trigger a massive increase in S-Cells, causing a physical change. That, he says, is Super Saiyan.
“Most Saiyans have some S-Cells, although not a great quantity,” Toriyama continued (via @Herms98). Thus, one of the reasons why Goku and Vegeta’s kids became Super Saiyans is that they inherited these cells. They have the genetic make up to become Super Saiyan.
This means that no matter how hard you train or how angry you get, if you don’t have enough S-Cells, you cannot become a Super Saiyan.