I think a lot of builders say this simply to avoid talking about the issue altogether
Obviously is it possible to build guitars for a living, but that does not mean that anyone is going to be able to do it.
The thing is that "building guitars for a living" is going to mean many different things to many different builders, since everyone has a different idea of what constitutes a "living," just as every builder has a different approach to, and relationship with their craft.
But, despite this wide array of circumstances, when the topic of "building for a living" comes up in discussion, most get a pretty homogenised vision of what that looks like, based on a handful of shining examples, so it immediately becomes easier to recite the meme of the starving luthier, and dismiss the goal as unattainable, than to address all the things that are really preventing you from taking that path anyway.
This is a totally valid and honest standpoint, and I think a lot of people would rather say it's just not possible, than to admit this to themselves.
It is something I have struggled with a lot, myself. I have had some major anxiety issues around this, and have often questioned whether I really wanted to continue.
There are so many things to get stressed about with an endeavor like this, and that alone is going to keep a lot of people from getting there.
And that's if you are making 3000 profit each one, after all shop expenses, not just the outlay for that instrument.
Money management skills are often an issue, but not nearly as devastating as time management problems. There are a lot of different acts to juggle in running a business like this, and usually one person has to do it all, as well as what the rest of their life requires.
Again, everybody's situation is going to be different here.
For me~
My partner works a full time job which basically covers bills, food, bare minimum living
My business provides a nice supplement to that, but probably still doesn't bring us up to official poverty level. We live out in a rural area in the southeast US, so our expenses are pretty low, but our lifestyle is
also pretty simple. We could live pretty well on poverty level income.
My son is grown up and on his own, but we have a daughter who is 11, so my time has to be balanced between my roles as parent, luthier, housewife, and small business owner.
My lack of time management skills messes each of these up in their own turn, and is not much more helpful in keeping them all going simultaneously.
Management skills, whether money, time, business, or whatever, are things that most artistic people tend to fall short on, and there is no one way of fixing that, since everyone does it in their own special way.
The real key is to be honest with yourself.
Evaluate and identify your strength and weaknesses, and own them both.
Fix what you can, adapt to what you can't, reinvent yourself if you have to.
It can be a brutally painful process, but better than getting called out on it later on, when you have been faking it the whole time.