Chains wear out and if the chain is not changed in a timely manner, it will wear the sprocket out quicker than normal.
A worn sprocket will also wear out a new chain quicker than normal. Worn sprockets and worn chains are plenty usable, but they'll be noisy.
In the pic posted above, the 44T sprocket on the left is worn out. The 36T is pretty worn, too. The 28T is complete junk.