The beauty of much of the networking terminology is that several of the most common words can be interpreted to mean different (and perfectly valid) things, depending on how you interpret the question.
Reading through the other thread and this question, I *think* you mean, "Why would use not use 192.168.1.x (et al) all the time?"
Most devices of what I call the "Plastic Router Class" default to 192.168.1.x or 192.168.0.x for the LAN subnet. Further, this is done with a subnet mask of 255.255.255.0, indicating that you can have 255 hosts on the IP network (though the physical LAN itself might breakdown if you have 255 devices all on one giant unmanaged network).
One advantage of sticking with whatever default LAN subnet is supplied with your router is that it is one less thing you have to manually configure our change around. A disadvantage of this is that many devices come with default IP's in one of these subnets.
Personally, I typically use 192.168.11.0/24, 192.168.13.0/24 and 192.168.15.0/24 for my "private" IP's. There is no significance to the 11, 13 and 15, they're just fairly uncommon.
As you hopefully know, you can't have 2 devices on the same LAN with the same IP and expect everything to work. Because LANs have become a lot more common, and people in general are more comfortable plugging things into networks (even if they shouldn't be), there is a high probability that at some point, probably years after you set everything up, that somebody is going to get a new multi-function printer thing, or a camera off Amazon, or whatever and plug it into the network. If that devices default IP conflicts with something else on your network, unpredictable things can happen, but they usually manifest in the form of really sporadic problems.
I'd rather that any random device plugged into a network by someone who is not quite sure what they are doing be logically isolated from the working devices on the network. It's not an outright guarantee that nothing bad will happen, but it will often prompt a phone call "I just got this Widget, and I plugged it into the network and my PC doesn't discover it the way it is supposed to". Maybe that call comes to you, or hopefully it goes to the manufacturer of that device, but either way it's a bit of cheap insurance.
In the end, any IP addressing scheme that lets all the appropriate devices talk to each other is perfectly fine, and no one set of numbers has any inherrent advantage over another set of numbers. It's mostly personal preference or corporate standards for how to set things up.