The math is a little tricky. Dr. Ray Ridley did a lot of work on this back in the early days of current mode control, but essentially a current-mode controller operating in continuous mode with duty cycle at or above 50% is not unconditionally stable, and a pertubation (change) in the load will cause the converter to break into a periodic instability that is self-sustaining - you see this as adjacent pulses being radically different from each other - narrow-wide-narrow-wide-narrow-wide...
Essentially, a current-mode controller is a third-order system with a low-frequency pole and a double pole at half the switching frequency.
Adding appropriate slope compensation to the current information can be mathematically shown to fix the instability by splitting the double pole (moving one of them to much higher frequency) making the system behave similarly to a voltage-mode control system - stable and easy to compensate.