You don't indicate whether you're installing the extractor into the crank with a wrench or your fingers. It's very common for them not to go in readily with fingertips alone, and if you find that putting a wrench on it lets you get it in there then you don't have to do anything further.
Look very carefully at the threads of the crank. Are there signs of stripping or cross-threading? If there is some damage, is it to just a few threads causing a high-friction spot, or is it all or many of the threads past a certain point?
I don't totally understand why this is, but the common way in a shop to touch up an M22x1 extractor thread (as opposed to replacing a destroyed one with a larger size) is not with a conventional tap, but with a much simpler and cheaper piloted chasing tool that looks like this:
They do a good job but you might notice it's pretty much the same thing as the outer part of a crank extractor plus some flutes to clear material and a reference guide, and the nature of various square taper cranks is that there's no guarantee that the extraction threads were precisely aligned enough in the first place that you'll ever be able to necessarily use the guide. (I've at least used them in situations where the guide was a no-go but it was fine in the end.)
Where I'm going here is that while there are no guarantees you won't destroy you cranks this way, if the damage is moderate or better then it's pretty reasonable to use your extractor outer bit as an impromptu thread chaser. What I would do is use a 90 degree scriber you don't have reservations about bearing down on to get into the threads and try to "clear a path" for it, doing some preliminary shoving around of errant or damaged material. Then use either cutting fluid or heavy oil to lube up the threads, guide in the tool as much as you can by hand, and then put a wrench on it and very gradually advance it. The leverage of the wrench will let you feel what's happening, i.e. whether it's totally stuck or able to make some progress. If you have some luck and it advances, do a little bit and then go back out all the way so you can clear any material, then go back in, repeating until you can work it back and fourth with no friction.