The legal category "property" is based on the concept of ownership. Ownership can be attributed to any human action that implies control over a rivalrous entity. A human body is certainly a rivalrous entity, meaning that only one person can exert control over a human body (or any of its aspects that are conceptualizable as discrete constituents of the bundle of property rights) at a time. Therefore, human bodies may be analyzed according to the same principles as scarce physical objects or other rivalrous entities.
Is ownership a moral category? According to Hans-Hermann Hoppe's deduction based in the ethics of argumentation, it would be illogical to argue that A. human beings are not self-owners, and B. that human beings have no right to own property.
According to my own argument (in the process of being constructed), a person who wanted to argue that human beings are not self-owners and should not have a right to own property would have to affirm two statements: 1. it is desirable that there be conflict over rivalrous resources, and 2. it is desirable that rules of justice be particularistic (i.e., different rules for different people). If one were not willing to approve of these claims, one would have to accede to the claim that justice should be based on self-ownership and property and with the understanding that self-ownership is subsumed under property ownership in general. (I will refrain from reproducing the entire argument at this point in the interests of focusing attention on the topic of this essay. Feel free to comment in the comments section.)
So, to deny the moral standing of property ownership is to affirm a preference for conflict over scarce (or rivalrous) resources and a preference also for different rules for different people. Against this, the proponents of the dichotomy between human bodies and other forms of property have only proposed a subjective preference that human bodies not be considered property.
Now, there is an important point that should be clarified: what is meant by moral? My arguments apply to that segment of traditional moral philosophy known as "justice theory." In other words, my arguments are based on the supposition that there is a need for rules for interactions between human beings that are related to the question of "Who should be allowed to do what with what rivalrous entities?"
It is possible to use the word "moral" as it was traditionally used in a religious sense: that is to say, rules that were arbitrarily determined by religious authorities and philosophers of religion. These rules could guide not only human interactions, but also how a human should act even if the question of conflict over rivalrous entities was not relevant to an action. Although the tradition of forming these rules based on religious precepts may be waning, their logical character has not changed in that they are still arbitrary and their basic assumptions are nothing but subjective preferences.
Thankfully, philosophy has advanced beyond the need to pay homage to unverifiable and arbitrary assumptions, and we can demonstrate that the "moral" precept that "people are not property" (short for "social rules should apply to people more than property") is unjust.
Finally, I'd like to clarify that "people are more important than property" may be a sound statement in one area of justice theory: namely, the study of sentencing (retribution and restitution). It is generally agreed among propertarians that the property one has in a human body is the most important property that a human being can possess, this for obvious reasons. Therefore, in the limited field of sentencing, the statement that human beings (human bodies) are more important than (other forms of) property is a correct and valuable precept.