From a storytelling standpoint it makes sense for Gohan to not have a drug-like addiction for fighting like his father, simply because having two characters that share too many similarities withim the same story seems uninteresting.

But speaking from a in-universe POV, i've seen many people say that Chi-Chi's strict behaviour is the reason behind Gohan's lack of fighting spirit, and given most mothers want a safe future for their children it makes sense for her to keep him away from fighting. 

However, to say Chi-Chi is the only reason about why Gohan isn't really a fighter is innacurate, since there are many event withim the canon that helped to establish this. Traumatic events that ended up being rooted withim Gohan's subconcious.

• At the young age of 4, Gohan was kidnapped by his own uncle. Sure, he gets rescued shortly after that, but his father died on the process (and with a huge hole on his stomach nonetheless).
  
• Then some green monster by the name of Piccolo took him away from his family only to leave Gohan alone for six months. After that said green monster puts him in a hell-ish training regime.
  
• Then the barbaric Saiyan warriors know as Nappa and Vegeta arrive on Earth, and Gohan has to fight them against his will. Suicide bombings (that one Saibaman and Chiaotzu), Ten getting his arm cut off and Piccolo's sacrifice (after being alone with him for so long he started like him) are some of the things Gohan saw with his own very eyes during the battle against the Saiyans.
  
• Then the Frieza saga happened... oh boy, where should I start? Seeing the massacre on the Namekians, the Ginyu Force, seeing Kuririn getting impaled by Freeza....
  
• Then we reach the Cell saga and nothing particulary traumatic happens to Gohan, until we reach the fight Gohan had against Cell. It was the first time Gohan actually enjoyed a fight, and how does that end? With his father Goku dying again.
  

Now, some people are going to say that Son Goku went through a lot of crap during his childhood as well. To be completely honest I haven't watched the enterity of OG Dragon Ball myself, but from what I saw the challenges that Goku faces increases gradually (level 1>level 2>level 3. etc), whereas Gohan jumped from level 1 to level 5 if you know what I mean. Besides, the pure-blooded saiyan grew up eating wolves in the forest and raised himself for a year or two. To Goku, survival is probably just what you do every day. It's not traumatic because it's all he knows.

Gohan on the other hand had five years of normal life, then about seven where super powerful monsters were trying to kill him and everyone he loved, then peace again. That sort of whiplash can mess a person up.

Don't take me wrong, I'm not saying that Son Gohan utterly hates fighting. The examples of Goku and Piccolo,as well as Artificial Human 16s iconic speech showed Gohan that fighting for justice is a noble cause.

First of all, let's start with that one fragment from the Saiyan Special Q&A that started it all.

Quote:Q: Do Saiyans train to fight?

A: Most Saiyans are born with a talent for battle, but they still need to be taught the trick behind flying and stuff like that. Of course, some kids manage to fly even without being taught. In Goku’s case, he was on Earth where people flying was simply unheard of, so he was pretty slow to learn it. Only a select few Saiyan children receive a short period of special training in order to acquire even greater battle power.

Q: Can anyone become a Super Saiyan if they train?

A: 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”.2 Once these S-Cells reach a certain amount, a trigger such as anger will explosively increase the S-Cells and cause a change in the body; that’s Super Saiyan. Most Saiyans have some S-Cells, although not a great quantity. The reason why Goku and Vegeta’s children can become Super Saiyan relatively easily is probably because to a certain extent they inherited a lot of S-Cells, and also because Earth’s environment is gentler and easier to live in than Planet Vegeta.[/align]

[Tori-bot] “Lately everyone becomes Super Saiyan so easily, but it is no simple matter.”

↓ And how does one increase S-Cells to become Super Saiyan?

A: Having a gentle spirit is the best way to greatly increase one’s S-Cells, but most Saiyans have trouble with this, which I think is why no Super Saiyans appeared for such a long time that they became the stuff of legend. However, one can’t reach the quantity necessary for becoming a Super Saiyan simply by having a gentle spirit, so a certain amount of battle power is indeed necessary. Looked at in this light, it’s easy to see why becoming a Super Saiyan came easy for Goku.[/align]

[Goten picture]  “He was able to easily become Super Saiyan thanks to inheriting lots of S-Cells!”

[Goku picture] “A gentle heart + high battle power resulted in Super Saiyan!!”

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http://www.kanzenshuu.com/translations/saikyo-jump-january-2018-we-asked-akira-toriyama-sensei-saiyan-special-qa/

As you can see, not only this article mentions that being gentle is a great way to increase S-Cells, but things such as a high battle power and inheritance (which probaly amounts to the same thing if we consider Trunks and Goten).

Caulifla is the only U6 Saiyan who transformed using the "back-tingling" method, and I wouldn't be surprised if we found out she was a hybrid later on. Either way, she inherited a high number of S-Cells, so at least now we have an explanation of why it came so easily to her (+ she's known as a prodigy!). But Cabba and Kale both needed a trigger in order to transform.

See? The S-Cells don't really change anything about the SS transformation.

Be really "pure," be really strong, get mad. The science behind it (see what I did there?) is still the same.

Gohan, Goten, and Trunks were all naturally really strong, and they are pure of heart (the first two were seen riding on the Nimbus), so they achieved Super Saiyan -- which is on itself, a biological quirk of a race of aliens, rather than a force of nature like Ki.