I think there are some flaws in your definitions, resulting in a mistaken conclusion. To the market anarchist, property is properly defined by human action, namely Lockean homesteading and voluntary exchange. As such, the socialist necessarily claims superior ownership over individuals when exercising his beliefs, meaning he is a would-be ruler.

In exercising authority over one's property, one is not claiming rulership over others, instead merely clearly defining the sphere where others would illegitimately be claiming to rule him. This standard is reciprocal and universal. In contrast, the socialist in attempting to create a universal principle instead removes any means of measuring where individual authority rightfully exists, and opens the door to tyranny.

The State and government are not synonyms. Government is a group of people who claim the authority to usurp the rights of others through a territorial monopoly in violence, basically like in your description above, but the usurpation of the rights of others is the point of trespass, not the assertion of the rights that were usurped. This distinction cause sthe rest of your argument to fall apart.