Fragile Wet Hair

A: While it is true that wet hair is far more fragile than dry hair, pulling a shirt or sweater over your head won't cause hair loss. I would still recommend towel-drying your hair first, if only to prevent saturating your shirt or blouse collar or turtleneck.
This rough friction roughs up the hair's outer cuticle layer, leaving behind a rat's nest of tangles. Some then add injury to insult by raking a fine-tooth comb or standard bristle brush through the mess, snapping dozens of weakened strands in the process.
When hair gets wet, its temporary hydrogen bonds break down. This allows the strand to stretch up to 30% to 50% beyond its normal length, but it loses much of its elasticity, making it easily snap at weak points.

This might make your theory about pulled-over clothing sound plausible, but because the cuticle scales lay flat like shingles facing downward (from root to tip), a shirt sliding down over your head glides over the hair with minimal friction. However, if you're wearing heavy, tight-collared, or high-friction clothing (like coarse wool), avoid repeatedly dragging it over wet hair. Also, pulling wet hair back into a tight ponytail or bun while getting dressed can cause traction tension on fragile, damp roots.
Actual hair loss requires damage to the hair follicle itself or an underlying internal trigger that forces hair into a shedding phase. If simply pulling a shirt over wet hair pulls strands out directly from the root, consider seeing a dermatologist to check for conditions causing weakened root anchorage. Otherwise, stick to gentle towel-squeezing (preferably with a microfiber towel or cotton t-shirt) and use a wide-tooth comb to detangle wet hair safely.
©Hairfinder.com
See also:
Can I use any towel to dry my hair without damaging it?
Should you not brush hair when wet?
How to minimize post-shampoo detangling