Cast your cares on the LORD and he will sustain you; he will never let the righteous be shaken.
The threat is humility. Or to put it another way, the reason Peter deals with the problem of anxiety is because he is dealing with the problem of humility. Somehow the command for humility makes the command to cast our anxiety on God more urgent, more needed.
Casting Your Anxiety on God Is Part of Humbling Yourself
The point is that casting your anxiety on God is somehow part humbling yourself. Casting your anxiety on God is crucial if you are going to humble yourself under God's hand and clothe yourself with humility toward each other. Casting your anxiety on God is not simply a separate thing that you do after you humble yourself. It's something you do in order to humble yourself, or in the process of humbling yourself.
There is something about humbling yourself under God's hand and humbling yourself before other people that makes casting all your anxiety on God necessary. Or to say it another way, there is something about casting your anxiety on God that makes humbling yourself under God and before others possible.