Butter and ghee aren't paleo, but non-paleo doesn't always equal BAD. Lard, tallow, and coconut are the closest to what our ancestors would have eaten.

" The amount of casein in butter is minimal and can often be tolerated without a problem even by individuals who are highly sensitive to milk and other dairy products."

The best fats for cooking are the ones lowest in polyunsaturated fatty acids, because PUFAs don't tolerate heating well (they are prone to lipid peroxidation). Like Melissa said, butter and ghee aren't exactly paleo, but it doesn't mean they're bad. Besides, cooking something in oil on a frying pan isn't paleo either.

Coconut oil, ghee, butter, palm oil and lard are all good choices. Apparently high oleic sunflower oil is low in PUFAs too, though I haven't used it myself.

I think I heard Robb Wolfe explain once that Cordain advised against animal fat back in the day because it was hard (and still is, for many people) to find grass-fed meat. So if you have only grain-fed high omega-6 meats available to you, staying away from the fat is a good idea. His evolution on this point may have something to do with grass-fed meat becoming more widely available.

Cordain's discouraging stance on saturated fats has "evolved" in recent years. See here.

The best fats to cook with are saturated fats, because they don't oxidize as easily under heat as the unsaturated fats do.

So, the best fats for cooking would be lard, butter, ghee or coconut oil.

MUFA omega-9 oil like olive oil is also OK, although it's not as good as the SFAs.

PUFAs like canola are bad all-around, and omega-3s are healthy when not heated, but they're very bad for cooking because they break down so easily.