Why is XOR called a controlled inverter?
An XOR gate has the following truth table.

 A  B | Q
------+---
 0  0 | 0
 0  1 | 1
------+---
 1  0 | 1
 1  1 | 0


I've split it up into two parts.

Can you see now where the name comes from?

You can consider that A is the control pin, and B/Q are the data bus being controlled.