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Some of the reasons they gave why people oppose homeless shelters in their neighborhood are;
Fear of crime and drugs coming into the area and feeling unsafe
A sense that the homeless may deserve to be there because of wrong choices, behavior, and etcetera.
Some just have no reason
Others say that the neighbors may not understand until they experience homelessness themselves.
Some responses were reasons why the homeless don't like living in shelters. They do not like having to follow rules that are set by the shelter or they feel imprisoned. Some of the answers suggested were to build individual homes for the homeless.
I know that one charity- Family Promise Chattanooga- in my area has a yearly fundraiser where people donate and rent a cardboard box for the night and camp out.