Jaime Lannister killed the Mad King right before he gave an order to burn half a million of King’s Landing’s population.
Jaime attacked Daenerys in madness right after she burnt most of the Lannister army, only because in his eyes, it was obvious to him that this new queen is unjust and crazy with power.
Jaime never wanted anything in the world, but to be with the one he loves most.
Jaime desperately still has hope that a peaceful time might come in Cersei’s reign after finishing the current war.
On the other hand,
Tyrion Lannister had this look on his face even before he notices Jaime.
Tyrion felt sorry for the Lannister army being burnt to ashes right infront of his eyes.
Tyrion wanted to surround Cersei till she gives up the throne peacefully.
To show the houses and lords of the South that Daenerys came in peace, and not with savages to repeat her dad’s massacre.
Tyrion watched as his house soldiers die in vain in a war that has nothing to do with them.
Daenerys literally won nothing in that battle, but she lost a lot.
She lost the respect that Tyrion had for her. She lost the respect of the South lords that Tyrion wanted to acquire. She lost the food and burnt it all, even though she needed it. She got her favorite dragon wounded. She got some of her Dothraki army killed. And all for nothing.
The realm can’t handle another Mad Ruler.
Jaime tried to save thousands, maybe millions of people, just like he did before, by attacking Dany.
Jaime still is a hero in the shadows, even if he’s too naive and even if he’s still making some wrong decisions.
He still thinks that he can make the world a better place, in a way.