You seem to be assuming that only government is capable of providing certain services (police, military, etc.). This is a very common assumption, but it only takes a little bit of pondering to realize that no proof or evidence exists to support this (others being banned from doing something does not equate to them being incapable of doing it).
A great place to start in understanding the fallacy in this line of reasoning is to accurately identify what exactly government is. IE: What characteristic differentiates 'government' from every other group of people?