Why do some politicians and interest groups favor protectionist policies while most economists oppose them?
Let me address the second part of your question first. Most economists do indeed oppose protectionist policies because the economics literature over the past two hundred years is filled with countless analyses of trade by countless economists with virtually all of them coming to the same conclusion: Trade benefits people! Economists understand that individuals engage in trade because both sides benefit: the buyer wants what he buys more than the money he gives up to obtain it, while the seller values the money he gets more than the good he is selling. This is true for people living across the street from one another, and no less true for people living on different sides of international borders.
Trade brings people together and gives them powerful incentives to keep the peace; protectionism pulls people apart and puts them in the mind to take by force what they can no longer acquire through commerce. Trade broadens consumer choice and reduces prices and thereby makes people wealthier; protectionism limits choices and raises prices and thereby makes people poorer. Trade spurs competitiveness, efficiencies and innovations; protectionism reduces competition, rewards inefficiency, and stifles innovation. Trade puts the consumer first, all consumers in fact; protectionism puts the producer first, particular and politically favored ones, in fact. Trade enhances the international division of labor and thereby fosters prosperity; protectionism hampers the division of labor and takes us a giant step backward to Robinson Crusoe economics.
Economists see the value of trade and the harm of protectionism because they understand economics. A few of them also believe in individual rightsnamely, that my basic human right to buy a car made in Japan is not mitigated one iota by General Motors' preference that I buy a car from them, any more than Burger King's desire that I buy a hamburger from them is reason enough to punish me when I buy from McDonald's.
A cardinal rule of economics that virtually all economists understand is that you cannot close the border to imports without closing the border to exports. If foreigners cannot sell here because of high tariffs, then they cannot earn the dollars they need to buy here.
Protectionism, moreover, is not a policy one nation can engage in by itself for very long, even if it somehow was beneficial to its people (which it isn't). When one nation raises its trade barriers, other nations almost always retaliate by raising theirs.
The bottom line of why economists are almost all opposed to protectionism is that they are looking at the big picture. They are considering not simply the effects of protectionism or free trade on only a few people or only in the short run; they are considering the effects on all people and in the long run as well as the short run.
Therein lies the answer to your question. Politicians and many special interest groups who favor protectionism are simply not being thorough in their thinking. They are not considering the effects of their policies on all people, nor are they considering the effects in the long run. They are like the idiot who observes a thief who has just robbed everybody in the neighborhood and who now takes his loot and spends it at all the stores at the local shopping mall. The idiot notices that the thief's spending seems to have stimulated the mall economy and made the shop owners very happy. Being an idiot, he concludes that the thief's act was somehow good for the general economy.
Politicians are not paid to be smart economists. They get paid and reelected if they've done nothing more than use the political process to hand out goodies to special interests who will vote for them, and demagogue the rest of an uninformed public into believing that they're doing us all a big favor.
Protectionists come in both varieties: the innocently naive but mistaken, and the maliciously selfish who are out to get something at someone else's expense and don't care about the consequences. In any case, the protectionist is wrong, and it is largely the duty of the economist to grab him by the scruff of the neck, shake him up a bit, and tell him, "Put your thinking cap on and start thinking about the harm you are inflicting on lots of people now and in the future."