In Animal Farm, why were the pigs so quickly accepted into a leadership role?
Simply put, the pigs are more intelligent than the other animals. While the horses struggle to read single letters and the sheep cannot read at all, the pigs are able to read and understand complex books. This gives them an edge in dealing both with arguments and with implementing ideas; the animals tend to argue from emotion, while the pigs can argue from two separate positions: actual knowledge, and knowledge of how to construct a confusing argument with only one reasonable solution.
It had come to be accepted that the pigs, who were manifestly cleverer than the other animals, should decide all questions of farm policy, though their decisions had to be ratified by a majority vote.
(Orwell, Animal Farm, msxnet.org)
The pigs are also seemingly higher in subjective status because it was a pig who came up with the philosophies of Animalism. Old Major was the instigator for the rebellious feelings that resulted in the Animal Farm's creation, so the pigs, sharing his species, are all elevated in public opinion. This allows the pigs free rein in making farm policies that benefit them more than the other animals, and to excuse and justify their acts with circular logic instead of rational discussion. The other animals are simply not smart enough to think through the issues; the animals that are smarter, like Benjamin the donkey, make no effort to educate the other animals or bring the unfair distribution to light. After Napoleon reveals his dogs, of course, power shifts from public equality to military.