Why not? Because the person with chronic anxiety and/or depression already knows it's all in their mind - at least, the psychological reaction is in the mind. No shit, sherlock.
But that's the thing: it's a reaction, an impulse from perceptions of the environment.
Just as anyone who heard a stick crack in a forest would immediately begin to feel anxiety, (heightened sense of awareness, increase in heart beat, shortness of breath, dilated pupils, a gnawing and growing feeling that something is wrong and a general inability to relax), the person with chronic anxiety (and/or depression) perceives something to be wrong with their environment. There is an acute feeling of dread, as if something bad is about to happen, similar to the feeling one gets in a horror film when the protagonist goes into the dark room unprepared.
It doesn't matter if these perceptions are skewed, biased, distorted, or inaccurate, what matters is that the person feels they aren't skewed, that they aren't biased, distorted, or inaccurate. Reassuring them that it's "okay" because you don't perceive anything wrong does little to help, just as you telling me that you didn't hear a stick crack in a forest would not generally reassure me. I don't think you see what I see, because if you did see what I see, you would probably have the same reaction as I do.
Typically my own anxiety revolves around an obsession with my responsibilities to others (worst-case scenario architecture and catastrophizing), as well as an obsession with doing something I do not wish to do (ego dystonic, for example, joining a fundamentalist church group despite being an atheist). Most people aren't going to take these too seriously, but I certainly do. The former is largely what I perceive to be a rational obsession, whereas the latter I fully know to be irrational, yet intrusive, thoughts.
Anxiety, like most emotions, is not entirely susceptible to rationality; even if you were able to give me a list of reasons why I am wrong about something, or how I'm not perceiving the world accurately, I would most likely retain an acute sense of dread, even if it has been diminished.
This is because anxiety largely revolves around the unknown, the uncertain. You are uncertain about what caused the stick to crack in the forest, therefore you feel anxious. It's just with chronically-anxious people that they perceive a threat where there may not be one, simply because they are not 100% sure.
In light of the inability to be completely certain, an anxious person will fall into a series of compulsions, meant to reassure them that everything is okay. Compulsions rear their ugly, insidious head when the anxious person continues to compulse despite the obsession being largely "rationally" dissolved. The obsession has moved on from simply a logical or rational peculiarity to a strikingly emotional, non-rational character, provoked by the very compulsions that were meant to dissolve the obsession in the first place. The compulsions metaphorically dig pathways in the brain, not so different from other habit-forming exercises. In this case, the compulsion becomes a kind of habit, one sustained out of fear.