There are many reasons to oppose capitalism. The most important one to socialists is that it exploits workers. But when we say that capitalism exploits workers, we don't just mean that a lot of them don't get paid enough (which they don't). We don't mean that they often lack health care and other benefits (which they don't). We don't mean that they don't have a fair say in what happens to their jobs and their company (which they don't). These are all of the liberal complaints with capitalism, and they are complaints that socialists share, but they aren't the exploitation that socialism is meant to address.
No, the exploitation socialists refer to can be summed up in two words: surplus value.
A man has money. The man wants more money. His money does nothing by itself, it has to be turned into capital, like an office and computers. The computers do nothing by themselves, either, they require the labor of people to operate them. These people work for the owner, and produce a surplus of goods and services, more than their own wages would buy. The owner takes this surplus value for himself as profit. The owner is taking the product of the labor of others. Profit is the direct result of unpaid labor -- profit is the direct result of exploiting workers.
Here capitalists object that everyone gets their share of the product. The workers get the portion their labor contributed, the owner gets the portion his capital contributed. Fair and square, right?
Wrong. The problem here is that the workers are being rewarded for what they actually do, but the owner is just being rewarded for a relationship: his relationship to the capital. The owner is being rewarded simply for granting permission for other people to produce, not because he contributed to production himself. This is apparent when you consider that if the workers stop working, production necessarily ceases. If the owner stops granting permission, production only ceases if people continue to recognize his authority to control the means of production.
And this is why socialists oppose capitalism and private ownership of the means of production. Socialists do not recognize the authority of some people to profit from the work of others without actually contributing to the creation of that profit. Socialists do not recognize the right of some to exploit others.