Removing kitchen tap limescale
3 Ways to deal with plumbing that has seized due to lime scale

1 More torque

Get the biggest wrench your space will allow and use it to loosen the plumbing.
Alternatively, you can try using a pipe to extend the leverage you have on an existing wrench.

2 Descaling


Go to the dollar store and buy some 'cleaning vinegar' (and a spray bottle if you don't have one).
Pour the cleaning vinegar into an empty spray bottle and close it.
Thoroughly spray the area with the lime scale
Wait 10 min
Repeat steps 3 and 4 until lime scale is satisfactorily removed


3 Cut and replace the fitting

When the other two methods don't work, or you have plenty of pipe to work with, you can use a pipe cutter, pipe saw, or oscillating saw to cut to the affected are and replace the fitting. 
This method is the one I generally use, as trying to salvage something with a lot of buildup is time consuming and not likely to re-seal well.

Going forward you'll want to address the reason for the scale build-up (water pressure too high / improperly sealed connection) and possibly think about installing a descaling filter on your water main to protect appliances and any fancy shower heads.