Why is it bad to mix brands of RAM.

Differing brands, and even types within a brand can have different properties on such features as the timing. Therefore it may negatively impact on the performance if one module has to drop its performance to that of the slowest.

It could even in the worst cases not work at all or cause damage.

It's bad only in terms of performance, as the faster ram module will downclock to the slowest ram module to make things even.

Of course, that's the case only if you're using the correct type of ram as stated by the manufacturer of the motherboard.

If you mix brands or models of memory, you will generally negatively impact your ability to overclock the memory. This can be really bad in cases where a CPU may have a locked multiplier, thus requiring you to overclock using the bus speed.

if you push the bus speed, it will also end up pushing the memory clock speed.

While you can do things such as lower the memory divider, you risk having the memory underclocked.

Another issue can be with memory voltages. If you have 1 memory stick that uses a lower voltage and another that uses a higher voltage, most motherboards will not allow each stick to have it's own voltage, instead you will end up with 1 memory stick running unstably because the voltage is too high or too low.