If they are distributed randomly around the shirts, it could be some kind of insect nibbling on them. That would call for deep cleaning the dresser drawers and maybe adding some cedar chips.
If all the shirts have holes in the same area, such as near the waist, it could be pressure from a seat belt, clothing, snaps on jeans, buckles on belts, rough spot on a counter top edge.
Most likely they are caused from washing and drying them with clothing that have zippers.
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