Trigger warning: Contains discussions of sexual assault
Chi-Chi and Goku perhaps have one of the worst relationships in the history of Dragon Ball as Goku time and again expresses no interest in spending time with her while she constantly pushes him to stop fighting altogether and get a soul-sucking job. Basically, they seem to be completely incompatible. While their relationship may seem unsustainable and downright odd, its origins are actually way worse than the current state of their marriage.
Goku and Chi-Chi have been together for most of their adult lives, and after getting married, Goku and Chi-Chi started a family by having two sons, Gohan and Goten. While Goku is a Saiyan, Chi-Chi is completely human so their children became a mix of the two species while having access to all of the powers of a full-blooded Saiyan. Once their children entered their lives, the difference in priorities between Goku and Chi-Chi became evident as Goku wanted to train his kids and help them master their Saiyan powers while Chi-Chi was primarily focused on their education and wanted them to be scholars who could grow up and get high-paying jobs. Even though Chi-Chi is depicted as being a straight-laced person in her adult life, she was originally a fearsome warrior as a child who was even able to out-muscle Goku on one occasion–though that story is far more tragic than it seems.
In Dragon Ball Chapter 12 by Akira Toriyama, Goku and Bulma are traveling around the world searching for Dragon Balls when they come across a location where they believe one Dragon Ball to be: Frypan Mountain. The mountain is ruled over by a monstrous man named Gyuumaou who initially attacks Goku and Bulma before he realized who Goku was. Gyuumaou knew Goku’s grandfather, Gohan, before the world-renowned martial artist passed away before the events of the series. Since he was related to an old friend, Gyuumaou asked Goku to do him a favor, and in return, he’d give Bulma the Dragon Ball they were after. Gyuumaou needed a source of mystically endless water to extinguish the fires surrounding his mountain from Master Roshi, and asked Goku to get it for him. However, Gyuumaou already sent his daughter, Chi-Chi, to retrieve that very same thing, so he also asked Goku to ensure Chi-Chi return home safely after the task was complete.
When Goku was seeking out the seemingly mythical Master Roshi, he spotted Chi-Chi and offered to give her a ride to Roshi’s before returning her home. While his initial approach was gentlemanly, Goku unwittingly assaulted Chi-Chi by grabbing her crotch to see whether she was a boy or a girl based solely on her anatomy. Chi-Chi is shocked and humiliated by this action and punches Goku in the face, telling him that what he did was not OK. However, after Chi-Chi scolded Goku on his inappropriate actions, she then perceived Goku’s assault as something that meant the two are now together romantically. Chi-Chi believed that since Goku touched her in that way, she had to become his bride–which is something that eventually happens.
Looking back at this early chapter of Dragon Ball, it seems as though Goku and Chi-Chi’s engagement unofficially began with Goku sexually assaulting Chi-Chi and then Chi-Chi confusing that assault with real feelings which made her feel obligated to marry Goku–an incredibly problematic and shocking origin that is way darker than most Dragon Ball fans know.