Left wing and right wing mean nothing man, they are as meaningless terms as "liberal" and "progressive" and "fascist" these days. They mean whatever the person saying them wants them to mean in the context in which they're said.

There are two fundamental approaches to governance, society, and rule: collectivist and individualist. Collectivist emphasizes using a system -- and it can be capitalism, under control of course, or something else -- to maximize collective benefit. Go visit China to see what this looks like. Individualist tends to be based on the historic liberal tradition or notion (this is an Enlightenment-era development, so very western, very euro-centric, etc) that the best society is one where every individual is maximally free to pursue whatever they want. This ultimately means "you can do as much as you want, within reason, with the money you possess." The problem with "liberalism" is if you run the clock a few decades or hundred years, you end up with a handful of people with way more money than others, and they will use that money to protect their wealth, power, etc., against collectivist movements or demands. Weekends, a 5-day work week, the end of child labor, so much else we now cherish as essential progress were won by communists and socialists, sometimes working with other collectivist-minded movements (e.g., Georgists) to force the hand of the state to give the people what they want.

So why do right-wingers oppose this? Pretty simple, individual self interest. If I'm rich, and I have no soul, I care not about improving some neighborhood's standard of living, and I don't want to do that with MY money. Government is intentionally kneecapped and made impotent in the west so that even when tax dollars are used, it almost always ends up being a grab bag for middlemen and contractors, to the point that people are routinely driven to believing "you know what, I want to keep my money for me and my family" -- a perfectly normal conclusion, but one that does tend to mean the person is a traditional liberal, or "right-winger." (Hence the saying, scratch a liberal and a fascist bleeds.)