When bridged mono, the load presented to the output circuit for each channel is halfed. So, if you have an 8 Ohm speaker wired to a single channel, the load on the amp is 8 ohms. If you take that same speaker and connect it to a bridged amp, the load to each channel of the amp is 4 ohms. So, if you put a 4 ohm speaker on a bridged amp, each output section sees a 2 ohm load and you have problems.
It really is that simple in practice, though the physics is more complicated.