Actually, the authors don't just assume their case against ownership. The present a rather convincing case against it. You can read their argument in a nutshell on p. 32:
"There is no market without government and no government without taxes; and what type of market there is depends on laws and policy decisions that government must make. In the absence of a legal system supported by taxes, there couldn't be money, banks, corporations, stock exchanges, patents, or a modern market economy - none of the institutions that make possible the existence of almost all contemporary forms of income and wealth. It is therefore logically impossible that people should have any kind of entitlement to all their pretax income."
In other words: The idea that we are morally entitled to our pretax income is incoherent, since our pretax income only makes sense against the background of an already existing market, and this market is possible only because of the existence of tax-financed government.
This argument is repeated several times throughout the book.