In my opinion, he was afraid that Asgard wouldn't accept him because he was a Frost Giant. He clearly didn't want to reveal that, Loki himself didn't knew until he held the Casket.

Because it's not really a choice. The tradition is that the title goes to his firstborn which was Hela but since she was too busy being in jail for being too bloodthirsty or whatever, the next in line was Thor.

^Both of those explanations are valid, imo.

While it would go automatically by tradition to Thor as the firstborn, I doubt Odin would've chosen Loki if he had the option, because of his heritage and how that would affect people's perception of him negatively.

I mean I guess the reason why is because Loki was his adoptive son while Thor is his biological son

I guess if you born on Asgard that means you will be next in line for the throne.

Since Loki wasn't I guess he couldn't been picked

Loki

is

not

worthy