All 6 Uses

contrary
in
Animal Farm
(Edited)

Others asked such questions as ... 'If this Rebellion is to happen anyway, what difference does it make whether we work for it or not?', and the pigs had great difficulty in making them see that this was contrary to the spirit of Animalism.
p. 17.1

contrary to = in opposition to
Do not imagine, comrades, that leadership is a pleasure! On the contrary, it is a deep and heavy responsibility.
p. 55.4 *

on the contrary = an expression used to strengthen denial of an idea
That evening Squealer explained privately to the other animals that Napoleon had never in reality been opposed to the windmill. On the contrary, it was he who had advocated it in the beginning, and the plan which Snowball had drawn on the floor of the incubator shed had actually been stolen from among Napoleon's papers.
p. 57.8

on the contrary = an expression used to intensify denial of an idea
Napoleon was well aware of the bad results that might follow if the real facts of the food situation were known, and he decided to make use of Mr. Whymper to spread a contrary impression.
p. 75.2 *

contrary = different
A too rigid equality in rations, Squealer explained, would have been contrary to the principles of Animalism.
p. 112.7 *

contrary to = in opposition to
Napoleon had denounced such ideas as contrary to the spirit of Animalism.
p. 129.4

Definitions:

(1) (contrary as in: a contrary idea)
different (perhaps opposite or mutually exclusive)

In formal logic, contrary propositions or contrary arguments describe two things that cannot both be true. They might be described as mutually exclusive. For example, a pet cannot be both a cat and a dog. It doesn't need to be either, but if it is one, it cannot be the other. So the statement that a pet is a cat and the statement that the same pet is a dog, are contrary statements.
(2) (contrary as in: a contrary personality)
disagreeable -- typically in reference to someone's personality
(3) (contrary to as in: contrary to)
in opposition to

You could also think of this as meaning, despite, or in spite of, or in conflict with; but since a common meaning of contrary is opposite, you many find it easiest to think of contrary to as in opposition to.
(4) (on the contrary as in: on the contrary)
an expression used to intensify denial of an idea
(5) (to the contrary as in: to the contrary)
with an opposite or different effect; or something with an opposite or different effect
(6) (meaning too rare to warrant focus)