Depression has different levels. Your average depression is just that, depression. I wouldn't say it can be "cured", but it can absolutely be treated. Not everyone is "cured" of their depression, they just learn new ways to live with and manage it. The reason I hesitate to say "cure" is because the meds we use are treating a chemical imbalance. The use of meds and therapy doesn't fix or cure said imbalance, it just helps correct it, often to the point where the depression is much more manageable.
Another level of depression is treatment resistant depression. This is the type of depression that absolutely does not have a "cure" and is almost impossible to learn to live with.
So people with either type of depression take it very personally, as it is a hugely personal issue, and find some of the other people's depressed thoughts comforting.
To a person with treatment resistant depression (TRD), the idea that depression can ever be "cured" is tough to deal with. When you've been depressed for so long, and someone tells you there is a cure, it sounds like they're invalidating your experience. Because there are the people who have been on 20 different meds, tried countless therapy sessions, and have even resorted to potential treatments like TMS or ECT. To be told there is a cure is almost like being told you just haven't tried hard enough to find it. I know that's know what's being said, but that's how it feels when you have TRD.
To a person with a more typical depression, the idea of a "cure" is necessary. It is the basis of all their hope. They need to believe that this isn't permanent, and their experiences haven't yet forced them into believing that it is permanent.
Really, all the confusion stems from the use of the word cure. Depression can be treated and managed to the point it really does feel like it was cured, though not for everyone. So is it really a "cure" or just an ongoing treatment.
That's when you get typically depressed people talking about how there is a cure and that suicide is a permanent solution to a temporary problem. And then people with TRD hear this, internalize it as self-blame, and talk about how if you can be cured you don't have "real" depression like they do.