I recently moved into a new apartment and need to remove the aerator tip on the Moen kitchen faucet to set up the countertop dishwasher I brought with me from my previous apartment. It was missing the aerator inside and had a bunch of mineral build up to begin with. I've tried everything I found suggested for this issue online and it just won't budge. I tried soaking in vinegar and spraying both inside outside edges of the piece with WD-40 to break up the mineral build up and any rust. I tried (clockwise from above) hand twisting, a wrench, and channel lock pliers both with a cloth and without since it was missing the actual aerator to begin with so I'm not concerned about scratching but it hasn't moved at all, all that I've accomplished is stripping the metal on it. Shy of replacing the entire faucet, is there anything else I can try?
If you look closely, many aerators have a couple flat spots on them, that you could tighten an adjustable wrench on to. That or a strap wrench would have been my first tool. But failing that, and the lack of desire to preserve the original finish, the curved jaw vice grips pictured above should work.
The next level, replacement wise, would be to file some flat sides onto the doomed aerator and use a wrench.
...and following on my comment, locking pliers would be my gripping tool of choice. this flavor with curved jaws:
Not this flavor with straight jaws.
However, for the level of stuck you have, I would also use a hammer, in conjunction with the locking pliers - put the things on so they are like this picture looking from above, quite tightly. Tap, don't beat (or at least don't start with beating) on the heavier handle with the screw adjuster (making this the unscrew direction is the point of putting on like the picture when looking down from above). If the jaws slide, stop, unclamp, tighten the screw, and clamp harder. The shock of the hammering will help to break things loose. Many small tappings may be more effective (and certainly less damaging to the tools and faucet) than just beating on it as hard as you can.
Things expand when heated, and metal is great at this...but the trick is to heat it without running the finish of the metal. If your hot water is hot enough to scald you, that may be enough to loosen it. Otherwise you could try wrapping it in a few layers of tinfoil and using a candle or a LIGHT dose of flame from a blowtorch. If you have a heat gun, one would be ideal, or possibly a strong hair dryer. Heat the stuck aerator part more than the neck of the faucet (So it expand more than the threads of the other piece) and then try to remove it with vice grips or pliers. You might be amazed at the difference. Also try CLR cleaner for the mineral deposits and use a small rubber sheet to wrap around the faucet while you use tools so you get a good grip without scratches.