Why do the entry doors to most homes open inward, while in most public buildings, the entry doors open outward?
The basic doorway in your home has a very simple structure: A large board is attached to a frame using a few "pin" hinges. This design has a number of advantages -- it is easy to build, easy to install and easy to repair. Of course, it is also very easy to disassemble -- removing the hinge pins completely detaches the door from the frame.
While this might help you out a good deal as a homeowner -- you can remove the door in order to squeeze in an over-sized couch, for example -- it's not something you want to make accessible to intruders. For this reason, the hinge mechanism needs to be positioned inside the house. With a standard hinge design, this means the door will open inward.
Public buildings have the same security concerns, of course, but they also have to consider other safety factors. Unlike a private home, a public building is likely to have large numbers of people in it. In case of fire or other emergency, these people need to be evacuated as quickly and easily as possible.
When a mob of people rushes an exit, it's very hard for somebody to open the door inward -- everyone pushes up against the door, and there is no room for it to open. For this reason, an effective emergency exit needs to open outward, moving with the force of the mob. This is also why a lot of emergency exits are built with wide "panic bars" instead of ordinary door knobs. The basic idea is to build the exit so even the most out-of-control mob will be able to escape.
To maintain perimeter security, public exits are typically built with concealed or protected hinges, which are much harder to detach than simple pin-hinges. These doors are more expensive to install and repair, making them impractical for residential use. And as long as you don't have an unruly mob living with you, these outward-opening doors don't offer any real advantage in your home.
Here are some interesting links: