A little perspective from a sound engineer who has run sound for a ton of bands, who is also a guitar player:
The truth is, most guitarists have their amps too loud. While it may give them the tone they want, it ends up causing problems for the audience. Guitar speakers are very directional in their sound, so if someone in the audience is straight in front of it they may be hearing ear bleeding midrange nastyness, while someone towards the side of the stage isn't hearing much of that at all. PA speakers, on the other hand, are designed to spread the sound out evenly throughout the room, allowing everyone to hear the same thing.
Having the amps at a reduced volume, and allowing the sound engineer to provide most of the room volume from the PA, allows for several things. They can put the volume at a good level that mixes with the rest of the band, and can adjust throughout the night to make it fit as things change. They can also EQ the sound so that it fits well with the rest of the band, allowing the overall mix to sound better for the audience.
So, if the goal is to reduce the volume coming from the guitar amp to the audience, but you don't want to turn down your amp too much, there are a few solutions. One is to get a smaller cab, something like a 1X12 (or even wiring up a larger cab so that you can turn off some of the speakers). Another option which works really well if you have monitors is to turn your cabs around, to face either the side of the stage, or even the back of the stage. Since the sound from guitar cabs is so directional, just turning it to the side can reduce the signal going out into the room significantly. A Hot Plate or other similar device works for this as well, as a lot of the fizzyness goes away once the preamp and power amp start to get pushed harder.
Now, your sound guy may be unreasonable, but it also may be that the venue wants volumes at a certain level, and that's just the way it is. If there are monitors for the band to hear themselves with, than it's time to start working on dialing in a good tone at lower volumes. Even if it isn't perfect, it will likely yield a better result than having the amp turned up too loud for the venue.
I know many guitar players will disagree with me, but my experience has always been that the band will sound better when most of the volume comes from the PA. Once the volume is all coming from the amps on stage, the sound person can no longer control levels and tones, and what you end up with is a bunch of instruments that may sound fantastic on their own, but don't gel well in the room, which makes everyone sound worse.
Now, if you are playing a show with minimal PA support (just vocals and a few other small things), this doesn't apply, and your amp needs to carry the room, but if you have a room with a good sized PA, that's where most of the sound should be coming from.