I can understand that if you once had low self-esteem, you decide to put a seemingly arrogant front. It's completely normal and something he'll have to deal with. And they can be tiresome...

But at the same time... I have to say, trying to change someone will hardly ever bring about the change you want in them, nor is it really an expression of love. You're coming from a selfish place, imposing yourself on him to be able to love him, when you should love him for him. It doesn't seem like he loves himself that much, considering his vanity. So you plan is to add an extre person (his partner) to that list of people?

Instead of withholding, or focusing on his negative aspects and trying to correct them, why not ignore? Why not look to other strong points and focus on those? Love and open hearts render more positive results.