Am not defending this law at all, but the thinking behind it is twofold:

1. you might be handing out tainted or expired food
2. the bigger issue: you are creating a "nuisance" on the property where you're doing it, as large groups of homeless people gather there. Some would say it's a safety concern, for example handing out free food at the corner of a primary school.

Again, I'm not agreeing with either point, but these are arguments I have heard from people who back such laws.

To the second point though, I've seen it firsthand. Salt Lake City tried to do a good thing by making the public library a homeless-friendly zone by handing out free food and allowing access to WiFi. This caused a large amount of homeless to hang out there all the time, and some of them would harass and attack non-homeless patrons of the library to the point that pretty much all of them stopped coming to the library entirely, and the area became a no-go zone.

The real issue is that a large amount of homeless people have severe mental illnesses (since public sanitariums all closed in the 70s). So where there are big congregations of homeless, there will inevitably be harassment and possible violence. Cities don't want people feeding the homeless at any old public building to avoid these situations, hence the laws, which allow you to do it only at certain places the city allows.