People don't get mental illness right.
Not even after they start having one.
it's a complex subject to understand.
And most people find hard to see the brain/mind/personalities/feelings of someone as something that doesn't "respond to will".
They think it's about willing yourself or that a medication will fix it.
Truth is, even when medication is taken, if the illness is severe enough:
Medication = numbing of this and that symptom + side effects from hell
Will power to get better = stress building over the frustration of *it* not working
Honestly, if you don't NEED the family, just let them unaware of what's happening.
Better that way.
But if you NEED them, and need to show why, then you have to come up with a way to tell them in terms they understand. For that, I think we can try to help, but you would have to be more specific...
But it can be as easy as saying "Mom, dad, I have a mental illness: This is called anxiety, this is called borderline. I have tid bit of that, a tad bat of this."
"When I do X, Y happens."
"I can't do this without that medication."
Saying you have a personality disorder might make them think you're just not wanting to be different, btw.
Just say you have borderline problems.