Of course, this concern is rooted in language itself. By positing one thing, we amplify its opposite. It's why postmodernists hate binaries. It drove ancient Taoism's admonitions not to look at concepts like "good" and "hate." It drove the background of Dostoyevsky's story, The Dream of a Ridiculous Man.
But it doesn't change the fact: By asserting a concept like "mental health," we start looking for ways we aren't mentally healthy. And because our minds are remarkably complex and largely can't be explained (and not remotely understood) by science, we can all find ways we aren't "mentally healthy."
And on top of that, we incentivize people not to be mentally healthy, either by coddling them or flat-out giving them money.
The result: More and more people find themselves mentally unhealthy. And the further result: They do start to become mentally sick. Even if they start out wholly as frauds who merely pretend to be sick so they can go on disability, they eventually become sick. It's the lesson of the "Let's Pretend" chapter in C.S. Lewis' Mere Christianity.