The adjectives controversial and contentious both describe something that provokes differences of opinion or disagreements. A controversial issue, statement, or decision is one about which the public has strong and divergent opinions, often longstanding and much-discussed, and not likely to be reconciled any time soon. A contentious issue or topic is one that causes conflict or strife, whether in congress, in court, or at the dinner table. A contentious debate or election, or a contentious relationship with your supervisor, would be marked by hard-fought disagreements, as would a contentious divorce or contentious custody dispute. A controversial figure is a public figure who does or says controversial things. Contentious people are simply argumentative types.
To approve is to speak or think favorably of someone or something: to approve the policies of the administration. In some uses, approve signifies agreement or consent; in other uses, approve conveys a more formal confirmation or sanctioning, as when the Senate promptly approves a bill. The synonym endorse is most commonly used to talk about official and usually public displays of support. When someone endorses something, they approve, support, or sustain that thing. You may hear of a newspaper endorsing a candidate in a political campaign, or, of another politician endorsing, or putting their name behind, a candidate. The putting of one’s name to something takes a more literal turn in other uses of the word: to endorse a check is to designate oneself as payee by signing it, usually on the reverse side.
To irritate someone is to excite them to impatience or anger. This verb is commonly used to talk about an emotional disturbance that is relatively short-lived and not terribly deep—it might irritate you, for instance, if someone refuses to answer a question. The synonym rankle implies continued anger or emotional disturbance. When something rankles you, it causes keen irritation or bitter resentment, the kind that builds over time or festers. Harsh criticism from a colleague might rankle you, or eat at you, long after it is uttered. Unpleasant though all of this may be, the term's meaning has softened over time; on entering English, rankle referred to the festering or putrefaction of physical wounds.