Why has there been (and is still) such strong opposition to the unions by American business management?
Managers will always be opposed to unions because unions drive up the cost of doing business. This is not necessarily about power or excessive demands on the part of the union (as is implied in the previous answer). Instead, it is simple economics. A company can reduce its costs and therefore its prices if it is not unionized.
Unions drive up costs by reducing the supply of labor. They limit who can take a job (by limiting it to union members and/or by imposing qualifications for the jobs) and they limit the sorts of work that the people can do (through union work rules). When the supply of labor is diminished its price will go up. This makes it harder for the company to make money.
This is particularly a problem in today's globalized world. American firms that have unions often have to compete against firms in countries that have lower costs. The fact that unions push up costs make these American companies less competitive.
Therefore, opposition to unions is not necessarily caused by power hungry companies or by corrupt or greedy unions. Instead, it is caused by the fact that unions necessarily drive up wages, thus making it harder for companies to compete.
This is a great question. Many companies are not supporters of unions for several reasons. In light of this, let me list a few of them.
First, there is the important issue of power. When people come together and can bargain collectively, there is great power. This power at times can be great as or even greater than the corporate structure. For this reason, many corporations and managers are not in favor of unions. There is something about human nature that does not want to give up power.
Second, in the past unions demanded a lot and within our economic climate, corporations claim not to be able to pay out as much. Companies claim that the American worker at times are too entitled and that companies in the past years gave out too much. In light of this, they claim that they cannot sustain such practices anymore. The reality is not clear.
Third, some of the people in America are also against unions for what they see as the abuse of the system. There are a number of scandals of union people who are protected by law for doing very little. I am sure that these are a minority, but when these scandals emerge, they somehow make it to the front page.