In the dojo, one of the things we stress is that the students be aware of themselves at all times. This awareness creates a sense of responsibility. When we see a piece of paper on the ground, "we have to" pick it up. The meaning behind "we have to" is the responsibility that is born out of awareness. Since we see something, we must act on it. There is a Japanese proverb that goes, "zen wa isoge" or that good deeds should be done quickly without hesitation.
A good student is one who has balance, both physically and mentally. Aikido is a martial art and thus because its techniques can be lethal, it requires a certain amount of personal responsibility. In order to be responsible, one must be aware first. As the old saying goes, "One has to know there is a problem before they can act on it."
If one is taught to be self-aware and notice things and be responsible for them in the dojo then they might be able to carry that over into their daily lives. If they can see it, then they can act on it and, hopefully when they do, it will be a natural act that is done quickly at the exact right moment and done with good character. To be unaware of oneself is to act without character and to be irresponsible. All martial arts teach responsibility because responsibility is the virtue that ensures that when we do act that we will act accordingly.