Split Personality?

[Morwen]

The entire premise of the book hangs on this plot device. If Sauron gets the ring then we all kiss out collective behinds goodbye. Except for a few things like
---- Sauron already had the ring
---- it did not protect him previously when he did have it
---- the power in the ring came from Sauron in the first place
--- even with the ring upon his hand, a man was able to cut it off and defeat him

Its an internal contradiction that is at the very heart of the plot.

where in the LotR is it stated that the Ring was supposed to protect him or that it operates as a protective device? Where is this suggested?

Where is it stated or suggested that Sauron while wearing the Ring is invulnerable to attack making it impossible for Isildur to in fact cut it from hand?

And if neither of these things is stated or suggested then how is it a flaw if the Ring doesn't do something that it's never said that it could do?