In the Dragon Ball universe, Saiyans is one of the most fearsome races of space warriors. They are known for their warrior drive and adaptive physiology that makes them extremely terrifying in combat. Despite their limited number, they have a massive impact on the universe that they inhabit. When faced with the fact that they might be extinct soon, Saiyans started having kids to ensure that their race survived.
Logically, it would seem that a person who is born half-Saiyan would have half the strength of Saiyan, but nothing could be further from the truth. In fact, half-Saiyan might turn out to be stronger than their full-blood parents, which might sound counterintuitive. But that raises an important question, why are pure-blood Saiyans portrayed to be more powerful than the half-Saiyans?
Saiyans are naturally gifted as fighters, and as a race of warriors, they push themselves to become stronger. They even become stronger with every near-death experience they have and undergo rigorous training to ensure that they become fearless warriors in the future. Therefore, Saiyans like Goku and Vegeta have become such strong warriors as they have trained and fought harder than anyone else. However, it is essential to notice the difference between half-blood and full-blood Saiyans.
The sons of Vegeta and Goku are powerful, and their human sides have not limited them in any way. Surprisingly, their overall power is even increased by their half-blood status. During the “Saiyan Saga,” Vegeta and Nappa mentioned that the children that they had on Earth might turn out to be too powerful to confront. Many instances prove that half-bloods are genuinely stronger. Gohan was regarded as a prodigious kid despite being young because of his raw strength. He achieved Super Saiyan 2 before anyone else, and during the “Cell Saga,” he even tapped into previously unknown potential to become stronger than his father.
Just like Gohan, Trunks, too, was able to surpass Vegeta and even proved capable of going Super Saiyan. So, the presumption that half-blood Saiyans are not as strong as the full-blood Saiyans is wrong because they have more raw potential than their parents. The only limitation is probably their lack of fighting drive, which ultimately limits their growth in several ways. So, even though half-blood Saiyans can become stronger than their parents, they are limited by a critical behavioral difference. Their lack of drive ultimately hampers their chances of becoming stronger than the full-blood Saiyans despite having impressive potential.