Correct. The arm and chain ring are pressed together and not intended to be separated. If the chain ring is loose on the arm, you can sometimes repair if you carefully center, and then use a hammer and anvil to swage back together.
What is the damage to the chain ring? Broken tooth?
It looks like a 1940s or early 1950s era crank, having a black chain ring and chrome arm. They often ran these with chain cases because the case would hide the black chain ring, so no need to plate.