Ring Modulation adds a constant frequency above and below the source frequency, producing non-integer relationships between the input signal and the new signal.
That's why it sounds weird, because both of the new tones will almost never be harmonically related to the input signal.
I don't know that much about ring modulation, but having read a bit about it, I think I love at least most of the uses of it I know. The guitar solo in Paranoid Android is one of my favorites in any record. But I love pretty much everything Jonny Greenwood has ever done.
That's why it sounds weird, because both of the new tones will almost never be harmonically related to the input signal.