A whole house fan draws air from the living space into the attic. The attic then needs enough vent area to exhaust the air to the outside (you can calculate the area required based on the CFM of the fan). You also need air coming into the living space through windows and doors to make up for the air being exhausted (failure to have this can result in pilot lights on furnaces and water heaters being extinguished).
What was his issue with your house?

Said it would have to be installed in the laundry room next to the garage (where part of the attic is) and that it would only cool off the garage, suggesting that there needed to be an attic overhead. Thanks for your input, Randy. Doesn't make sense to me.

We would really like a whole house fan (that cools the house, of course). Does anyone have any input on whether or not a whole house fan would work in our home as described above? Thank you!