Go to plan B.

If it's a lime scale buildup, use five tablespoons of vinegar (doesn't really matter what kind) and enough salt so the salt all dissolves. Start with small amounts of salt and increase until saturation point where a few grains don't dissolve. Add a TEAspoon of vinegar and Bob's yer uncle. Let that sit in the faucet for a half hour, and if you drink beer that's a good time to have one. If you can agitate it with a toothbrush or something like that, do so--NOT the beer, the faucet!. Rinse with clean water. (Take a few glasses with you.)

GENTLY, try leftie loosie once again.

Plan C: redo plan B.

If that don't get it, you require a for-real plumber kinda guy or gal.

At no point is it worthwhile to strike the faucet with a hammer. If you do, ya better be wearing safety glasses.