If we don't, we'll eventually die by either a natural disaster, population collapse, OR WAR.
The more humans expand, the more people born. The more humans there are, the more people are working to advance technology and make new scientific breakthroughs, which means that humanity will advance at a much more rapid pace.
It's a pretty basic notion. If humanity expands to across the Milky Way Galaxy, and eventually outside of the galaxy, extinction of humanity would essentially become an impossibility.