The differences between a Prime Minister and a President differ from state to state. A country can have one or the other, or even both. A prime minister is the leader of legislature but must also answer to the legislature and could even be ousted from it. A President does not have to answer to the country's legislative body except in certain circumstances. In USA, the President is the head of the state, whereas in UK, it is the Prime Minister (they do have a Queen, but she is merely a symbol).
Maybe it's because not everyone can cope with each other after such a long time. Maybe not everyone has great social skills after living together for awhile.
