Everybody buys oil and everybody borrows money. If the price of oil goes up, we call that inflation and the central bank uses monetary policy (rising interest rates) to reduce inflation. Why is the price of money (i.e. interest rates) different from the price of any other commodity in regards to its impact on inflation? Does not a rising price of oil in itself cool the economy in the same way as a rising price of money? If we need to spend more to drive our cars, then we can spend less on televisions?
If everybody borrows money, where can you borrow money from?
In what unit do you denote the price of oil, chocolate, or cows? Well, in units of money. So calling interest rates the price of money doesn't quite make much sense.
You can think about it as the price of money today in terms of future money though. So an increase in interest rates makes money today more expensive in terms of future money, which is the same thing as making future money cheaper in terms of money today. And if future money gets cheaper, more people might "buy" future money (usually, we call that saving).
The more future money people buy with money today, the less money they have left for oil, chocolate, and cows. But we already have all the oil, chocolate, and cows around. So that people still buy these things, oil, chocolate, and cows have to get cheaper and the price level for goods and services measured in money today goes down. Less inflation.
While money can be considered a commodity, the comparison you are making with oil prices is not exactly accurate. The price of a commodity increases inflation, because it goes into the cost of what people consume. The price of money is deflationary, because it decreases the amount of money available to people and companies to pay wages and investment. Think about an oil company in a small country. The oil company raises the price of the commodity it produces, gets more money in its account, can pay its employees higher wages, who then go out and consume more. If the company wants to invest and the interest rate is high though, it will need to pay more interest, i.e. pay more to get the money to make the investment. The higher price makes it less likely for the company to invest. It may not choose to do so, wherefore the companies it would have paid to build, for example a new oil well, do not make money and won't be able to pay their employees higher wages, who then won't have the ability to consume more.
Money is not something people consume in and of itself. It is a means of consumption, whereas commodities are consumed. That is why one increases and the other decreases inflation.
Hope this helps! Happy to answer questions in the comments obviously.