Capitalism is the pursuit of money for its own sake, specifically via private ownership of the "means of production," which is a fancy way of saying: all the money that is created or captured by an activity goes to a limited group of individuals, even though the individuals that created or captured the money mostly aren't in that group.
Capitalism is a feature of a society, and is permitted or not permitted by that society's government. The main reason some people like the idea of using capitalism to structure economic enterprise is that it generally allows some individuals to accrue more money than others, and these people like to imagine that they can be among those individuals. The main reason other people don't like the idea of using capitalism to structure economic enterprise is that most people are not among the group that benefits.
There are other strategies, such as socialism, in which the means of production are owned collectively by the individuals engaged in production. In a socialist economy, the government provides services and support to its citizens and their enterprises according to a publicly-controlled set of priorities. Nearly every government and economy on earth functions via a mix of socialist and capitalist instruments, and most discourse about one versus the other is mostly concerned with how much of each is in the mix.
Capitalism specifically incentivizes actions that benefit oneself over actions that benefit other people. When your social imperative is to accrue capital, you are more likely to do that than to forego it or give it away, because it makes your life better, and that's how people are a lot of the time. Unfortunately, the downside is that most people do not have any way to accrue any significant amount of capital, because it is much easier to accrue when you already have some. So, capitalism may be good for some participants, but as a natural consequence, it is bad for most.
Capitalism also incentivizes acting for profit over acting for moral good—a good example is healthcare. In places where access to medicine and doctors is socialized and therefore available for cheap or free, a sick person can just go to a doctor and maybe get better. In places where it is privately owned, such as America, an arrangement between the government and a set of private organizations results in access to doctors being gated behind membership in for-profit healthcare clubs that partially defray the cost of care, called "insurance providers," who seek to make money by betting that the amount of money they receive from any member is more on average than they have to pay doctors and medicine providers for services they render to the member, and they justify the cost of the membership by pointing to all the people they employ to facilitate (or complicate) the exchange of money between themselves and the doctors and medicine providers for the services provided to the member. This system makes it prohibitively expensive for many people to seek medical care, with or without the membership, and as a result, many people just get sick and die instead. And that's capitalism!
Because every person who benefits from capitalism is outnumbered significantly by people whose lives are made intolerable by it, we consider capitalism to be really dangerous.
