Everyone grumbles about rules, whether it’s doing the chores at home, or having to make small talk in social situations. But grudgingly, we accept that at least some of them are useful, and probably necessary. The discussion around government regulation is similar—most people accept that governments should set some form of framework within which we lead our daily lives. We just can’t agree on what it should look like.
The point of regulation is to make sure that all the individuals that make up an economy are acting in a way that is fair, safe, and above-board. If the government declares, for example, that all meat must be inspected and graded before being sold, then it’s doing that because it thinks there’s a risk that otherwise, private meat sellers will sell bad-quality produce in the interest of maximising profit and minimising cost.
But for a government, which has to worry about the health of its citizens and the trust its consumers have in the products available to them, minimising cost at the expense of its citizens' well-being is problematic. So by setting this rule, it’s changed the context in which the private economy operates to make sure that it's in everyone's best interests (or at least that's what it's supposed to do.)
So in a way, the government is shaping the market. That’s what makes the term government intervention a slightly misleading one. Governments and the privately owned parts of the economy are so intertwined that it’s difficult to separate them out and claim one is intervening in the other – it might make more sense to think of the government as helping shape the web of rules that it takes for the market to function.