People often cross the street to avoid encountering suffering people who are begging for money. It’s not that they don’t care (if they didn’t care, they would just walk by), it’s that they are bothered by the suffering and would rather not encounter it. Usually, escape is even easier.
I don’t think it’s empathy that makes them cross the street. It’s trying to avoid it. Knowing that there but for the grace of god go I, and it’s uncomfortable to feel that vulnerable. So we avoid the empathetic response.
