According to Grammar in Use, we tend to use present continuous to describe current global problems as in your sentence.
Although I think this distinction falls under a more general category which is the usage of present continuous to describe an action happening around now as in
I'm getting fat.
The climate is getting warmer.
I'm learning spanish.
Yes, increasing population rapidly is happening everyday but it's not something that has been around for a very long time. Actually we can say it's happening everyday these days.
When you say, "The population of the world is increasing very fast"
You emphasize that this is going on right now and it's perceived like a warning
You say it's happening at your time and it's a current phenomenon.