The right words in the right order.

I like using the term mental health, because if I refer to someone as being mentally ill by saying "You're mentally ill" or "S/he's mentally ill" it gives off the impression that I am being mean and putting them down, and I suspect that's why people began using the term mental health in the first place, because it's neutral. 

 I don't understand. It doesn't mean anything on its own unless you add a qualifier, such as poor, good, or illness, wellness. How do you actually describe their mental illness? What words do you actually use?

I just use the term mental health, and if I was asking about someone's mental health, I would not use qualifiers, because heck if I know if that person has poor or ill mental health, unless they decide to tell me what's going on in their life. I can't just assume the status of their mental health, because I don't have the same mind as they do. I wouldn't know unless they've told me.

And I don't even know if that person would like me describing their mental health for them, as being "poor," or "unwell," or "ill," because they might find that I'm being judgemental and offensive, and that's my reason for not doing it.

But if I was talking about my own mental health, I would use all the qualifiers and descriptive words as much as I'd like to, because I'm just describing myself. 

I just use the term mental health, and if I was asking about someone's mental health, I would not use qualifiers, because heck if I know if that person has poor or ill mental health, unless they decide to tell me what's going on in their life. I can't just assume the status of their mental health, because I don't have the same mind as they do. I wouldn't know unless they've told me.

And I don't even know if that person would like me describing their mental health for them, as being "poor," or "unwell," or "ill," because they might find that I'm being judgemental and offensive, and that's my reason for not doing it.

But if I was talking about my own mental health, I would use all the qualifiers and descriptive words as much as I'd like to, because I'm just describing myself. 

I'm going to use language that is suitable for me and what I'm comfortable with. This has nothing to do with winning and losing. Just like some people are fine with swearing, others are not. If you'd like more descriptive language because you find the term mental health to be too vague for you, you can choose to add qualifiers if you'd like to. I just described my reasoning for choosing not to, but you don't have to agree with it. 

Hippopotomonstrosesquippedaliophobia said:

"Are you mentally ill or something?"

So the bullies win? We change our language to accommodate their bullying. Makes perfect sense.

You can use language in a that you're comfortable with. If you want to use qualifiers to describe your own mental health, then by all means do so. 

I've stated this earlier, but people have used the term mental illness in negative ways when describing someone else, to bully and harrass them in the past "Are you mentally ill or something?" This is why I prefer to use the term mental health, and not everyone is comfortable with talking about their mental health condition publically.  

Hippopotomonstrosesquippedaliophobia said:

I just use the term mental health, and if I was asking about someone's mental health, I would not use qualifiers, because heck if I know if that person has poor or ill mental health, unless they decide to tell me what's going on in their life. I can't just assume the status of their mental health, because I don't have the same mind as they do. I wouldn't know unless they've told me.

Your reply makes no sense to me, I'm afraid.  It would appear you have your won story about mental illness and mental health going on and you've wrapped yourself up in some imagined world where it's not okay to talk about mental illness for fear of offending people. But we've strayed far from the original topic of the post.

These are two grammatically correct English sentences:

I'm 35 and I have bipolar disorder.
I'm 35 and I have mental health. 

They are not equivalent in meaning. The second half of the second sentence although syntactically correct, it is semantically redundant without a qualifier. Unless, the speaker is making a declarative statement that they have a mind and that their mind has the capacity for health, which is generally agreed to be the case for all humans. 

Similarly,

We talked for a while about his bipolar disorder.
We talked for a while about his mental health.

The second of these two sentences is not an equivalent for the first one either. The second is a general statement. We talked about all manner of things relating to his state of mind, healthy or otherwise. 

Lastly,

How is the new treatment for your bipolar disorder working out?
How is the new treatment for your mental health working out?

Here again, the second sentence is at best vague, and at worst deliberately evasive. I take many treatments for a number of mental health disorders and I also practice yoga and mindful breathing. Which are you asking about? 

We all understand why people dumb down their language, but, here's the deal: they're not helping anyone by doing it (quite the opposite, they're perpetuating guilt, shame and awkwardness). Not only that,  but it's childish and silly too. If you're unable to communicate directly with someone about their mental illness without struggling with your own sensitivity and/or dumbing down your language so as not to offend them (I don't know anyone who is offended by addressing their mental ill health directly, by the way) then perhaps these are conversations you shouldn't actually be having with them in the first place and would be better sticking to topics more appropriate to the degree of closeness in your relationship.