If you train at a school that mainly caters to pilots that eventually want to fly commercially, you'll see lots of emphasis on actually using a checklist. Because that's what you do in a B737.
That's not completely true. What most GA pilots, clubs and schools often fails to understand is the difference between a procedure and a checklist. While it is true that you use a checklist when flying commersially, it is not used for EVERY single occasion. A procedure is what you do from memory. If deemed needed there's an associated checklist that you do after. This may contain none, some or all of the items stated in the procedure, but normally the most important items that will catch you out if omitted. For example an incorrect flap setting might potentially kill you on take-off, while a forgotten taxi light will not. The previous will be on the checklist, while the latter wont.
Upon speaking to said brother, he believes checklists should be out, used and referred to on every task, to avoid any doubt that I had missed something.
Ask your brother to try to manually fly an aircraft during a very turbulent instrument approach night time with strong and constantly changing crosswind component and in the same time read a 15 item checklist. Or indeed flying cuircuits in a densely trafficated uncontrolled aerodrome together with gliders and microlights, all with different speeds.