Why does the One Ring prevent Frodo from throwing it into even an ordinary fire that can't possibly harm it?

Near the beginning of The Fellowship of the Ring, as Frodo learns the true nature of Bilbo's ring from Gandalf, Gandalf challenges Frodo to throw the ring into his hearth. Though Frodo has been able to set aside the ring previously, and though the fire can do no harm to the ring (which had in fact been in this fire only shortly before and not even gotten warm), Frodo finds himself incapable of putting the ring in the fire.

Why? Why does the ring prevent this symbolic act that can not possibly hurt it?