I suspect he wants to do it because it makes sense to him from an electrician point of view with concerns about under sized return neutrals, balanced loads in the breaker box, etc, but what he is likely not taking into account is the very limited capacity of this generator and how wiring it up 120/240V effectively splits it into being 2 120V generators with half the total output on each since it sounds like you have no 240V appliances that can run on the 16 amps at 240V that this generator can provide.
Let me put this in other words, wired 120/240V split single phase you are in effect getting 2 buckets of 16 amps each to draw from, instead of one bucket of 32 amps. Lets pretend you have a big chest freezer that draws 9 amps, a window air conditioner that draws 10 amps, and a refrigerator that draws 8 amps, plus a few CF light bulbs that draw less than one amp each, and maybe a modern TV that draws an amp or two, and a notebook computer that draws an amp. When wired 120V only you get a bucket of 32 amps at 120V, so 9+10+8+1+2+1 =31 amps so no problem it is under the rated 32 (real world may be 35 or so, but you get the idea). Now lets make that two buckets of 16 amps, 9+10 = 19, oopps you are over, hmmm 9+8 = 17 ooops your over again, hmmm there is no way to get there and power the fridge, freezer and air conditioner at once. For a reasonable work around to this problem see my post #8 in this thread.