Not caring what other people think

I used to think I was the sort of person who didn't care what other people think. I was wrong. I was the sort of person who wanted other people to think he was the sort of person who didn't care what other people think. A very different critter.

Vices

The virtues support each other in two ways: (i) having one helps gain another; (ii) each helps to achieve the ends of the others. In regard to (ii), note that it is easier to achieve the goals of prudence if one is chaste, sober and eats in moderation, to achieve the goals of generosity if one is prudent and brave, to achieve the self-knowledge that humility aims at if one is wise and sober, and so on. This is partly distinct from (i).

The vices, on the other hand, support each other in sense (i), but hamper each other in sense (ii). Thus, laziness may lead to gluttony (having nothing better to do, one may just eat) and lust may lead to greed (in order to impress potential sexual partners): having a vice helps one gain another. But, in fact, the goals of the vices hamper one another. Lust is expensive, and hence hampers the goals of greed. Wrath makes it harder to make money and keep sexual partners. All the vices, including vanity itself, hamper the goals of vanity by making one appear ridiculous. Conversely, sloth and cowardice hamper the goals of all the other vices.

So, while type (i) support among the virtues is a delightful thing, because the virtues also help to achieve one another's goals, type (i) support among the vices is a baneful thing, because the vices hamper the achievement of one another's goals, but nonetheless the vices lead to one another.

This is a fine, and very broadly both Kantian and Aristotelian, answer to the question of why be virtuous.