Companies and individuals are most certainly able to create "money" on their own. You can issue all the debt you want, as long as you find a willing counterparty and sign your own name to it. It's balance sheet expansion.
For example, you go to purchase a new car, and sign a note telling the dealer that you will pay the price of the car, plus interest, over five years. You've created an asset out of nothing, for which the bank is more than willing to pay the dealer cash for. People and companies create such assets every day. There is no magic to issuing your own liabilities, which is what the Fed does when it prints money.
Other companies besides "banks" (savings and loans, credit unions, etc.) can. Other other companies and private individuals only can't in the sense that there are rules governing this to prevent abuse, and if you jump through all the hoops required to do that, you have become a bank, savings and loan, credit union, or some other entity allowed to do it. Banks, etc., are just the name given to entities that have met the requirements to engage in particular activities.