Why does Krishna want us to be detached from the fruits of our work? (Bhagavad-gita 02.47)

Because he wants to ensure that our care and our consciousness are distributed proportionately. He wants our work to be not just functional — providing us the results — but also transformational: helping us to change ourselves. 

When we focus too much on the external results of our work, and if we succeed in getting them, we may become arrogant and self-congratulatory. In contrast, if we don’t get the results, we may become depressed and self-condemnatory. Such obsession with external results can cause unhealthy changes in our consciousness, irrespective of what the specific result is. 

However, if we see our work as a means to offer our consciousness and our heart to Krishna, then we will be able to do our best in all situations, even in those situations where success seems remote because the odds are against us, as well as those situations where success seems easy and we may become complacent. 

With our consciousness absorbed in Krishna in a mood of service, we will become purified and our hearts will become more receptive to receive Krishna’s mercy and thus become further attracted to him. When Krishna urges us to offer him whatever work we do in a mood of devotion (09.27), the preceding verse states that are more important than the things we offer is the mood in which we offer them (09.26). This emphasizes that Krishna is concerned not so much with the fruits of our work or even our work, but with the devotion in our heart that is expressed and enriched by our working in a mood of devotion. 

One-sentence summary: 

Krishna is more interested in what happens to you while you work than the results of your work.