If you can mine money whenever you want how does the price of every bitcoin not diminish?
The answer to your question can be found on the Bitcoin wiki.
It's true that everyone can mine, but the amount of coins that are up to be mined by miners is controlled by the Bitcoin protocol.
The difficulty of mining a "block" is adjusted automatically (every 2016 blocks or ~ 2 weeks). The adjustment is made by all miners using a transparent calculation. The adjustment aims to retain a rate of approximately 1 block mined every 10 minutes.
Additionally, every ~4 years (or 210000 blocks), the reward for finding a block is halved.
Taking this two things in account, the reward for mining a block will become zero after 6930000 blocks or ~136 years. (It becomes zero because the precision in which bitcoins can me measured is too low.)
You may think that people will stop mining when the reward becomes too low, but you have to keep in mind that miners also get the transaction fees from the transactions they verify in their blocks. Currently the accumulated fee is only a fraction of the total reward, but as the reward decreases (and Bitcoin raises in value), these fees will (hopefully) become a sufficient incentive to mine.
Because the economy is limited to 21 million coins. They are created at a slow and regular pace that controls the amount of coins that are released at one given time. This is considered to be a deflationary system. The key aspect is that it is not easy to mine Bitcoin today nor will it be going into the future. To accumulate any amount of it by mining you need to spend a lot more on hardware than most folks are willing to invest. Low end mining on personal computers is no longer profitable and will actually cost more in power than you will ever see in returned Bitcoin.
I don't think the statement that everyone can mine is true. Sure, anyone can turn on a computer and set up their CPU to start hashing, but they will never generate a block and at the current difficulty they won't even get any shares in a pool, because the shares will be invalid by time they submit it back to the pool.
Currently, in oder to to mine, you at the very least need a bad ASIC-based miner. The worst on market I think is a 10 GHash/sec device which will return something around US$2-3/day which is not nearly enough for anyone living in any remotely developed country to live on. You are also assuming people would never want more money than they have currently mined which I believe to be a false premise.