Keep in mind, Han was promoted for the mission on Endor, so he wasn’t a general during ESB. The rebellion kind of promoted people as needed (or just straight up willy-nilly, see Lando being given a rank of general or whatever.)

Also, like in rebels, they promoted a teenager to “lieutenant”…. Because he was a half-trained Jedi… (yeah that went well,)

Further, after Hoth Luke was off at dagoba doing Jedi training; and while not shown, there was probably some time there.

Also, banging one of the main leaders gets you faster promotions than being the sister of said leader.

Han was a graduate of the Imperial Military Academy before being discharged for saving Chewbacca from slavery.

He was awarded the Corellian Bloodstripes during that period of time.

Unless the new Canon retconned all of that away.

Luke was basically a kid, not general material

Luke is a 19 year old kid with a gift for piloting small spacecraft.

Han Solo is an adult with actual command experience.

Han had previous military training, both in Legends and the new Disney Canon.

Luke may have fired the shot that took out the death star, but don't forget it was Han's support that allowed him to survive that long. Seconds before, Han took out Vader's escorts, also knocking Vader out of the way.

"General" might sound like an inappropriate rank if you compare rebel ranks to modern organization ranks. But remember rebels die a lot. Maybe they needed to promote someone.

Combat ability does not equal command ability. Point Luke at someone and he'll ruin their whole year, but he's not good at leading people into combat or organizing groups of soldiers.

Han was already a Captain of a ship and crew, capable of that kind of complex 'Generalling' as demonstrated by supporting Luke's run on the trench.

Luke was a flyboy kid off the farm, albeit a savant.

Edit. And further into the lore, the rebels would have needed people capable of leading other large groups of people to success. So they would tack on promotions or immediate ranks to retain that talent, but at levels they could use and trust.

Promoting a savant to General and giving him whatever groups of troops to achieve goals, ia much riskier than promoting the already somewhat proven Captain.

Luke was lined up for General in the short term anyways, iirc. At least in the EU canon.

I bet Luke put in a request for Han to be a general just to mess with him.

It wouldn't surprise me to learn that making him a "general" was a negotiation chip used to get Han to stick around.

I don't thinks that's written anywhere. But that's my head canon based on the characters as we know them at that point in the story.

Han brought a fast gunship to the party. That counts for something!