sheet of..., counter for flat thin objects or sheets
枚 centers on counting flat, thin items like sheets, leaves, or pieces of paper. The meaning 'sheet of...' is a natural extension of this counter use.
枚 combines 木 (tree, wood) with 攵, which is a variant of 攴 (a hand holding a stick). The original sense likely involved a wooden tally or counting stick, which later extended to counting flat objects.
Picture a wooden board (木) being struck (攵) to mark it as a tally for counting sheets. Each strike represents one flat item counted.
For マイ, imagine counting sheets of paper and saying 'my' for each one: 'my sheet, my sheet...' The sound 'my' cues マイ.
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counter for thin, flat objects (e.g. sheets of paper, plates, coins)
the number of flat things
handsome man
comedian; actor who plays comic roles
enumeration
monolith; large slab of rock
double-dealing; duplicity; equivocation; double-tongued
large sum (of money)
bivalve
(wearing) nothing but a pair of underpants
one (thin, flat object); one sheet
one step higher; one better; cut above; one up
one step higher; one better; cut above; one up
(place) just beneath; (area) directly under; what lies immediately below (the surface); (being) one step below
to participate in (as a member); to get involved in
leading player; prima donna; box-office star
playing with a handicap of one rook or bishop
univalve
three flat objects (sheets of paper, pieces of cloth, etc.)
filleting a fish (into boneless left and right halves and a piece with the skeleton)