I read the system is designed in such order (correct me if I'm wrong) that only 21 million bitcoins can be created.
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Actually the most that can be created would be 20999999.97690000
Most people just round up to 21 million when talking about it because it's easier. Due to some issues early on, there are some bitcoins that were unmined (and now cannot be mined), so the total will actually be less than 20999999.97690000.
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That is correct, but the system is designed to require a consensus to make a change. If every user agrees that more bitcoins should be mined, then more bitcoins will be able to be mined, but convincing every user to agree to such a change is an insurmountable task.
When a miner "solves" a block and includes the mining reward, he broadcasts that block to all the peers he is connected to. Every peer validates that the block conforms to the protocol rules before they add that block to their blockchain or relay it. This happens for every peer on the network (both miners and wallet clients). So if a subset of peers refuse to recognize the increase in block reward that is necessary to mine additional coins, they will simply ignore the block and refuse to add it to their own blockchain or relay it.
If you could get a subset of miners and peers to agree to accept the increased block reward, the blockchain would split. You'd have one group of users on the "original" bitcoin with a fixed 21 million bitcoins. They would only accept valid blocks as defined by the original protocol, and would never even see the blocks creates by the other group. Then you'd have a second group of users on some new blockchain that allowed more than 21 million coins. They might try to call their network "bitcoin", but there would be a disagreement as to which system was the "true bitcoin".
There would be a lot of confusion as some merchants chose to accept the "new" bitcoin, and some only accepted the "old" bitcoin. Users would try to make payments not realizing that the merchant they were paying was on the other system. Eventually after a lot of chaos, at least one of the two systems would likely die off as users migrated toward the one that had the most support.
Thank you for the summary