To encourage growth. If money is continually losing value, you have to continually work harder to outpace the loss. This encourages workers to keep working, and encourages businesses to keep innovating.
Although recent years have been a puzzling exception, it is typical for real interest rates (nominal rate minus inflation rate) to be positive. If someone is inclined to just live off their accumulated savings, this is just as possible with inflation as without, as long as the real interest rate is the same. It is true that the value of savings tend to be destroyed in episodes of hyperinflation, when real rates don't keep up, but hyperinflation is certainly not a road to a well functioning economy.
Were they finit 2000 years ago as well?
Are you infinitely dense? (I am not; I can't prove it, but I suspect you are less than infinitely dense.)
Stop spreading this shitty nonsense about limited resources please.