What is drive strength a measurement of?
The more current you source or sink through a pin, the more the voltage deviates from the ideal voltage.

Here is what the datasheet of some random microprocessor says about the relationship between output current and output voltage (you should find such specifications in any datasheet):

 

The question is not so much how much current the pin can handle (if you go near the absolute limit, your circuit is likely to fail anyway), but how much of a voltage drop you can tolerate.

Furthermore, a higher drive strength can supply the needed current faster when switching, which means that the voltage also switches faster, i.e., you have shorter raise/fall times.
This implies that higher drive strength can result in increased EMI.