I like this one, keeping it simple and logical; and nothing better than a little bit of self-refuting combo, aye?
"Although I’m not a utilitarian, one thing I find interesting about this philosophy is it can be self-defeating. That is, if a philosophical mindset other than utilitarianism tended to produce greater aggregate happiness than if everyone became utilitarians, utilitarianism would suggest switching to that mindset.
Put another way, if everyone following a rights-based theory of justice resulted in greater aggregate happiness, a strict utilitarian would suggest we follow a rights-based theory. Even if utilitarianism were 100% correct, it may not be the best approach to take if a simpler philosophy resulted in better happiness-increasing decisions."