I often see homeless people huddling together on street corners, which makes me feel sympathetic. Although I am not the one culpable for their leading such meagre lives, I cannot help but feel bad about having so much of what they do not. When my sympathy gets the better of me, I stop in front of them and hand them some change. But I am too diffident to chat, because I cannot sense the kind of equality that I hope for due to our inequality in economic condition. Perhaps, deep in me, I feel that only when I myself live in penury can it be possible for me to feel some genuine empathy.

Culpable - responsible is better for the topic

You use a lot of gerunds/progressives.

I often see homeless people huddling themselves up in street corners, which makes me feel sympathy. Although I am not the one responsible for their leading such meagre lives, I cannot help feeling bad about my having so much of what they do not have. When my sympathy gets the better of me, I stop in front of them and hand them some change. But I do not know what to say to chat, because I cannot sense the kind of equality that I hope for due to our inequality in economic condition. Perhaps, deep in me, I feel that only when I myself live in poverty can it be possible for me to feel some genuine empathy.

I totally disagree with you. Empathy is to feel for someone, you do not have to live in the same situation to feel for that person. You are aware of these people, you feel compassion, sympathy, and it is not your fault it is simply the way it is. It is kind of you to offer your change but please do not feel uncomfortable about having so much while they have so little. Homelessness is a complex issue, why doesn't he or she get a job?
Whatever their reason the fact the you are not homeless, have what you have, does not affect their lives one bit. I have heard some opinion somewhere that the wealth should be shared equally and I totally oppose that view. If I chose to give some money to someone, a charity or a stranger on the street then that is my choice. If the government took my money to share with everybody then what is my incentive to work.
In conclusion I admire your compassion, but please don't feel bad because you work hard and your parents worked hard to give you opportunities these homeless people do not have. You are a good person of that I have no doubt.