Use basic math to help explain it to him. Since you are dealing with a circle (pipe), the cross section of the pipe is calculated by multiplying the radius of the pipe squared times pi (3.14). So if you double the size of the pipe, you bascially get 4 times the amount of cross section, which you can equate that to almost 4 times the flow capability as well.
Some quick number crunching, a 3/4 inch pipe has a cross section of .44 sq inches and a 1 inch pipe's is .79 (a 1/2 inch pipe is .20 or .2x4=.8 thus 4 times the area by doubling the pipe size from 1/2 to 1 inch). You would only get slightly more flow from TWO 3/4 inch pipes than only ONE 1 inch pipe.
You also need to factor in some friction of the water flowing thru the pipe. The smaller the pipe, the greater the loss in flow from the water's friction with the sides of the pipe, this is an even bigger factor the longer your pipe run is. If you start adding a bunch of elbows, the flow reduction really gets bad, they can really knock down flow especially if you start with a minimal pipe size. Ask someone from your volunteer fire department about this and how much more water they can flow as the hose size goes up. Same concept here.
So, not only do you get a much greater flow capability with the larger pipe, you get less frictional loss of the flow and thus you can deliver many more BTUs by only increasing the size of the pipe by 1/4 of an inch. The increase in cost between the pipe sizes is a small price if the 3/4 is already marginal and does not work out and he has to dig everything up again.
I considered 1-1/4" when I did my install due to my long main run (225 feet one way), but the price of that size pipe jumped considerably over 1 inch pipe. I ended up using 1 inch Pex-AL-Pex because its nominal inside diameter was larger than 1 inch standard PEX so I gained a little bit by doing that. I got it for less than $1/foot. My pump has never been above medium speed even during the coldest periods here.