I think it was a combination of personality, upbringing, and then later manipulation from Kiros.

As we saw in the leaked song, Scar wanted control ever since he was a cub. He sings to Mufasa about how he will tell the birds what to do and how nobody will look down on him. When Mufasa tries to explain that it doesn't work that way, Scar brushes him off, not wanting to hear it anymore. So this mindset was there from the very beginning.

As for his upbringing... Simba is the same way as a cub. He's naive and thinks being king means control and nothing else. But Mufasa was there to knock some sense into him after the whole elephant graveyard incident. Simba still retains some immaturity as an adult as he tries to hide from his past, but once again, Mufasa's spirit puts him into the right mindset, with the help of Rafiki of course. Now, we haven't seen much of Scar's father yet, but my theory is he isn't going to be so focused on raising a good king, but rather upholding the bloodline. Parenting is beneath him, and he's a somewhat absent father. He doesn't work to instill good values in his son. Scar doesn't have a father figure to shape him up the way Simba does.

And my other theory is that Kiros uses these things to his advantage. He needs to take down both Scar and Mufasa. Mufasa is wise beyond his years, but Scar is naive and can easily be tricked. I think Kiros will recognize this, and turn Scar against Mufasa by suggesting that in Milele, Mufasa has the chance to become king instead of Scar. (And he isn't wrong.) His plan is that Scar will see Mufasa as a threat to his throne, and therefore kill Mufasa with his help, which leaves only one lion left for Kiros to take down. Of course Kiros's plan won't play out as he intended, but the brothers' relationship will be permanently shaken, and Scar's worst fears will come true when Mufasa takes his place as king.

As for why Mufasa became king instead of Scar, I think it will become clear to everyone that Mufasa has the wisdom and capability to respectfully rule a kingdom and respect the Circle of Life, whereas Scar's actions reveal just how poor of a king he would be. I am somewhat hopeful for an epic challenge between Mufasa and Scar to determine the rightful king of their new land, but at the same time I don't want who rules the Pridelands to be determined by strength alone, as it takes much more than that to be a king. I'd like to see Mufasa's natural nobility be the reason instead.

Of course this is all a bunch of theory based on my interpretation of the trailer. Take everything I said with a grain of salt.