Creative Tips For Removing A Rusted Faucet (Without Hurting Yourself)
Sometimes the difference between the right and wrong ways to do something is simply a matter of destruction. If you need to save whatever you're working on, it's not a good idea to destroy it. But when it doesn't matter, things get simpler. You will have noticed that the most careful carpenter can give in to absolute abandon during demolition; this is because things aren't being saved, and can be destroyed. So it is with everything, including the kitchen sink ... or in this case, the kitchen faucet.
It's not uncommon for the locknut that screws onto the faucet's threaded lower body or valves to get stuck, thanks to everything from rust to hard water to electrolysis. It's kind of a built-in flaw in the process: a leaking faucet (or a faucet that hasn't been properly sealed) is more likely to need replacement, and is also more likely to get corroded and therefore resist replacement. How you go about getting one unstuck depends on how willing you are to destroy the faucet. And by the time you've spent an hour under a sink working your way through a checklist of possible solutions, you'll probably be pretty willing to destroy it.
If you happen to have a retaining bracket secured by your locknut and it's corroded into place, your best bet is prying it off or cutting it off right away. Note that your faucet might also have a retaining clip. These can usually be pried off with a slotted screwdriver and moderate cursing.
How to remove the faucet without destroying it
Step one is to remove as much of the visible corrosion as you can with a wire brush. Regardless of your ill intent toward the faucet, the right place to start is always the correct tool for the job. In this case, that tool is usually either a faucet change-out tool like Ridgid's EZ Change Plumbing Wrench or a large basin wrench like Tekton's Telescoping Basin Wrench. If you have access to both, you might find that a long basin wrench works best since it has a T-handle to give you leverage while working in very tight spaces. Try first tightening the nut a little, then loosening it. Movement in either direction is likely to break loose the nut.
If the wrench doesn't work at first, you can try some chemical helpers. If the problem appears to be mostly hard water deposits, wrapping the works in a plastic bag filled with vinegar is reported to do the job... though it seems like the challenge of securing the bag in such limited space might cause most people to move on to the next step. That next step is probably the use of penetrating oil like Liquid Wrench or CRC Screwloose Super Penetrant, which purport to work its way into threads better than standard lubricants. Note that you should never use penetrating oil when the faucet is hot from a previous effort. After waiting the prescribed time, try your wrenches again, with mild cursing if necessary. A few light taps with a hammer or wrench, or perhaps a few accidental taps with your forehead, might help the oil penetrate.
Remove and destroy the faucet, or at least the retaining nut
It's perfectly reasonable to try all of the above steps even if you don't care about damaging the faucet, but it probably makes sense to skip any steps that require a trip to the hardware store for tools or lubricants. When all of the tricks above fail, and we must assume they will sometimes, we enter the territory of potentially damaging solutions. Try adding heat with a hair dryer or heat gun (a propane torch can be used with extreme care). Then have a go at whacking the assembly with a hammer, or better yet, hold one hammer against the nut and whack the other side with a second hammer.
If you have one, now's the time for having a go with a nut splitter, a manual tool that cracks the nut, but you're unlikely to find one big enough for a single-handle faucet nut. A nut splitter might work for smaller escutcheon retaining nuts such as the ones on sinks secured by both their hot and cold valves. Failing that, it's time to cut the nut off and move on with your life. You can do this awkwardly with a hacksaw, awkwardly and dangerously with a reciprocating saw, or fairly efficiently with an oscillating multitool fitted with a bimetal blade. Any blade will probably do for a plastic retaining nut, though you're unlikely to have made it this far down the list if your locknut is plastic.