I can't rescind my right to property? How can I give someone a birthday present???
(Hint: consent)
Actually, to give your property away is to exercise your right of property. Your right of property is not just to hold something in your hand, it is to dispose of it according to your will. That, by definition, is what the right to own and control property is.
To follow your logic, you should be able to throw away your right to liberty. This, Alan Keyes also states, is impossible if this right is unalienable. For, if you throw away your freedoms, and you do everything you can to undermine the laws that protect your own liberty, you are not just affecting yourself, you are affecting all other persons.