A washer skips its spin for two big reasons: it couldn't drain first, or it can't safely spin — an unbalanced load, a failed lid/door switch, or a worn drive belt.
A washer must drain before it spins, and it must sense a safe, balanced, closed-up machine before it ramps to high speed. So 'won't spin' is usually a drain problem, a balance/lid-sensor problem, or a worn mechanical part.
Check these in order. The first accounts for most cases.
A heavy, bunched, or oversized load throws off balance. The washer detects the imbalance and refuses to spin fast to protect itself.
If the water didn't pump out, the washer won't spin. A clogged pump filter or drain hose shows up as 'won't spin'.
Top-loaders won't spin unless the lid switch confirms the lid is closed; front-loaders need the door lock to engage. A failed switch stops the spin step.
A stretched/broken belt or a worn motor coupler lets the motor run while the drum barely turns.
Follow these in order. Stop as soon as the problem clears.
Open the washer, unbunch the clothes, and balance them around the drum. Remove a few items if it's overloaded, then restart the spin.
Check for standing water. If water remains, fix the drain first (pump filter / drain hose) — it won't spin until it drains.
Top-load: press the lid switch by hand and listen for a click; no click means a failed switch. Front-load: make sure the door latches and locks.
Rock the washer — if it wobbles, adjust the feet so all four sit firmly. An unlevel washer trips imbalance protection.
With power off, check the drive belt for cracks or looseness and the motor coupler for wear. Replace if the motor runs but the drum won't.