Disagree

v. have different opinions, differ; be unsuited

A controversy or dispute is a matter of opinion over which parties actively disagree, argue, or debate. Controversies can range in size from private disputes between two individuals to large-scale disagreements between societies. Perennial areas of controversy include religion, philosophy and politics. Controversy in matters of  theology has traditionally been particularly heated, giving rise to the phrase odium theologicum. Controversial issues are held as potentially divisive in a given society, because they can lead to tension and ill will. Some controversies are considered taboo to many people, unless a society can find a common ground to share and discuss its people's feelings on a certain controversial issue.
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Verb
1. be of different opinions; "I beg to differ!"; "She disagrees with her husband on many questions"
(synonym) differ, dissent, take issue
(antonym) agree, hold, concur, concord
(hyponym) dissent
(derivation) disagreement, dissension, dissonance
2. be different from one another
(synonym) disaccord, discord
(antonym) match, fit, correspond, check, jibe, gibe, tally, agree
(hypernym) be

(v. i.)
To fail to accord; not to agree; to lack harmony; to differ; to be unlike; to be at variance.
  

(v. i.)
To differ in opinion; to hold discordant views; to be at controversy; to quarrel.
  

(v. i.)
To be unsuited; to have unfitness; as, medicine sometimes disagrees with the patient; food often disagrees with the stomach or the taste.
  

kou3 shi4 xin1 fei1
The mouth says "yes", but the heart says "no".
To be double-faced.