WARNING: The following contains spoilers for Dragon Ball Z: Kakarot, available now.
Goku has never been what you'd call a good father. Maybe it's his obsession with combat. Maybe it's because he's dead or in recovery half of the time. Maybe it's because he confused marriage as a type of food. Whatever the case, Goku is absent for much of Gohan's life, providing little support for his son.
Dragon Ball Z: Kakarot, the newest game from Namco-Bandai, focuses on the character's downtime, and, in doing so, expands on the few moments in Gohan's life where he is with his father. We learn from these actions that, yes, Goku can be a loving father under the right circumstances.
Goku, the Bad Father
If you've seen Dragon Ball Z: Abridged, then you know the running gag: Goku is never with his family, prioritizes food and combat over loved ones, and Gohan sees Piccolo as a father figure more than Goku. Dragon Ball Super seemed to only reinforce this point further since Goku would rather hang out with Beerus than with his own family. In fact, when Gohan asks Goku to watch his granddaughter, Piccolo knows more about how to raise the young girl than Goku.
This isn't to say that Goku is the worst father ever. Far from it. But every other father in the anime, from Vegeta to Gohan to even King Cold, are there for their children in ways that Goku is not. This is in part due to the focus of the series. Dragon Ball Z is an action-heavy franchise. Even in the filler material such as during his training with Gohan during the Cell Saga, or the non-canon movies, Goku always seems to take second place to Piccolo in Gohan's eyes in the fatherhood department.
The Changes Made By Dragon Ball Z: Kakarot
Dragon Ball Z: Kakarot doesn't contradict any of the established canon of the series. Rather, it just builds upon it. In the game's tutorial prologue, we see an expansion of Goku and Gohan's relationship before the first episode. We see Goku taking Gohan out on a camping trip to gather supplies for Chi-Chi to make a meal. This scene establishes two core elements, even before we move onto the dialogue: that Goku helps Chi-Chi raise Gohan and spends quality time with his son.
Furthermore, Goku talks to Gohan and tells him stories about his adventures. Most specifically, he talks about Piccolo, his days with Master Roshi, and his experiences learning how to fish with his tail. He teaches Gohan how to fish as well, using either his natural tail or an artificial tail.
These moments, as expected, grow fewer and farther between over the course of the game, due to Goku either being dead, recovering, or in transit for the remainder of the saga. However, these moments establish one core thing: when Goku can be a good dad, he is a good dad.
Why Is Goku a Terrible Dad Otherwise?
Goku is a naive person. He seldom knows the right thing to say or do at any given moment. Because of this, he's probably not the best suited for really any situation that requires social interaction. However, he seems to be mostly good-hearted. Even in the series proper, when Gohan is kidnapped by Raditz, he's horrified and does all he can to save his son.
The problem is Goku's priority is fighting. He loves combat over all other things and is fueled by an all-consuming need to fight stronger opponents. At the start of Dragon Ball Z, as far as Goku knows, he is the world's strongest. Piccolo was the only one who could ever rival his strength, so, without the drive to push himself even further, he relaxes. The game even implies he's grown lax with his training. Without the threat of someone stronger lingering over him, Goku takes it easy and gives his family the time of day.
But when the Saiyans arrive, Goku's world is opened up in ways he never imagined before. After learning of a race of warriors all stronger than him, how could Goku not become obsessed with fighting again? And from there, Goku spends much of his time on-screen training, fighting, dying, healing and traveling, giving birth to the old meme: Goku's just a bad father. Thankfully, though, Kakarot has finally provided some context to improve his standing with fans.