I was thinking "bonus points for making a closed loop", but the first one I tried formed just such a loop and fast.

Rihanna is hotter than Beyonce.
Beyonce is hotter than Rihanna.

Monasteries, if not entire religions, have been founded on mysteries less deep.

Hey man, take a look at something named Prolog, you might be interested ... ;-)

Tom Lehrer hates Nader.
Nader hates Microsoft.
Microsoft hates Google.
Google hates your website.
Your website hates me.
Me Hates It.
IT hates women.

...

But noone, apparently, hates Tom Lehrer.

[don't ask why i started with "Tom Lehrer hates". it's kinda complicated...]

If women hate no-one, will that solve your chain?