Bitcoin as a financial system is made impractical in the long term by the fact that it is limited in the total number that can be issued. After the last one is issued, the intent is for the value of them to simply go up.
A Bitcoin is the solution to a hashing problem for which the ease in calculating a solution goes up with the size of the search space. In a very large search space it's easy to generate a solution, but as the search space becomes smaller you have to spend more time hunting around for a correct solution.
As more solutions are found, the people behind bitcoin validate that 'coin and then shorten the length in bits needed for a valid solution. They have a fixed number in mind that they want to base the currency on, and as the number of solutions found approach that number, they have been shortening the length so that they will eventually have exactly the number they want, and finding new solutions will take an astronomically long time.
There's nothing preventing them from increasing the valid length of solutions and letting people find more. They have explained countless times that this is how they can have actual inflation in their currency.
Countless times of explaining this to the public, and yet people continue to repeat bullshit they've heard "somewhere on the internet" that matches their woldview.
It's no wonder they're having trouble - they're concentrating on their project, but losing the war against propaganda.
That's a totally inaccurate means of explaining this.
The difficulty of finding a solution scales as the network grows, it has nothing to do with the amount of currency in it. Mining continues once the full amount has been released, because mining is about transactions, not block rewards. Once the total amount of the currency exists, then mining is rewarded by transaction fees as there is no more block reward.
The nameless "They" cannot increase the money supply. The entire network would have to vote to fork the code onto a new system to change the monetary limit. There is no "they" that have any control over the network, the only people who control the network are 51%+ of the miners.