The Reverend Natural Light wrote:

So I talked to him, he said he'll use 1/4 hardy board. He said it's
like a cement board but the particles are finer. I asked him if he can
do 1/2 hardy (or cement) board and he insist those are used on walls
and not on floors.

Yes. According to the instructions, 1/4 is stronger than 1/2.

He did not talk about a layer of plywood under the bardy board, and I
didn't ask him either since I am just reading this now. Is a 1/4"
hardyboard enough? How important is the plywood layer? He said there
will be another layer of cement (thinset) on top of the board so
having a 1/2" cement board is too tall.

The subfloor is the most important part of the job. The tiles will
crack if it's not right.

Like Mike said, 1 1/4" solid wood with any layers glued and screwed
together. Thinset and nails/screws securing the 1/4" hardiebacker.
And that's a minimum if the joists are solid.

The contractor insist that a plywood layer is not suitable for my
case. He said when he does new constructions he uses 3/4" plywood
because the sub-floor is not as strong as older homes so the plywood
is needed for structural needs. The wood subfloor you see in the
pictures are pretty thick and these types of homes don't need a layer
of plywood (mine was built in 1960). On the adjacent rooms where there
was hardwood floor, the hardwood sits directly on top of the subfloor,
there were no plywood in between... but hardwood is probably
differentn from hardyboard and can flex somewhat.

ah crap.

Raymond