The Athenians were a blind-following people, Socrates was one of the world's greatest thinkers. He offered questions, challenged people's thoughts, and treated life with the great question of a 4 year-old: WHY?
Socrates idea that philosophy calls on us to care for the soul is an important one for us to even consider today. Philosophy is the investigation of truth or principles. If the soul is merely pleased by entertainments it is a shallow soul. If the soul is not exercised because a man's work is rote or merely brain work, it remains a shallow soul. If the soul is given opportunity to know, to explore the truth of a principle, to understand then there is room for growth, and growth is good.
The soul is that which finds something to believe in. If we don't cultivate that, we lose our humanity.
I spent my last summer in Haiti. It is dirty, disgusting, gross, and I didn't like my enviornment. But, I got to teach English to school children and just love on them. This fed my soul. It didn't feed my physical need of comfort. It didn't feed or stimulate my brain for my own learning of new information. I wouldn't have gone to feed my soul had I not believed I could be of service and help to those kids.
Hope this helps. That is a great piece to read and registering the difference between mind, body and soul is always difficult.
Before starting to analyze Apology, note that the accounts by Plato and Xenophon differ considerably, and that neither is likely to be a verbatim transcription.
The theme of care for the soul isn't, in Platonic philosophy, precisely about the "feeding of the soul" in a 21st century sense. If we read Apology along with Crito and Phaedo, it refers to cultivating the rational aspect of the soul, and preparing for the separation of soul from body. Love for other may work anagogically in Plato as a step towards return to the divine (e.g. Diotima`s speech in Symposium), but it is not an end in itself, but rather a step to be passed through on the way to something more important.
Note that intellect (and especially mathematics) is crucially important in developing the soul, as it is through reason that we understand the forms, while the sense only perceive the particulars.