Running two amps together may give you an awesome sound, but doing so can result in phase cancellation. This occurs when similar frequencies from separate sound sources are played together, which are exactly or partially opposite one another. This is also known as 180 or 90 degree phase cancellation respectively. The problem with cancellation is that it gives an unpredictable and inconsistent tone, essentially neutering your overall sound.
In context, think about it this way... If you're playing either a riff or a chord progression with an ABY unit splitting your signal into two, what you're playing is doubled and those frequencies will oscillate at the same speed. However, those frequencies will be slightly different, as they are emitted through different amps with their own unique tonal characteristics. Those simultaneous frequencies may then end up fighting one another if 180 or 90 degrees out-of-phase, which you certainly don't want! Sometimes this is worse with similar amp combinations, but it may not occur with a more diverse pairing.
If a power struggle materialises with the opposing frequencies cancelling each other out, you'll be left with a flat and thin sound. So to avoid this, many ABY boxes will feature a "polarity reversal" switch. What it does is quite obvious from its name. It will take one of the signals and reverse or invert it, so that the peaks of the second waveform will occur closely in unison with the other. That's science.