I think it is misleading to think of psychologists as being able to 'read people's mind'. For that, you would need a mystic. There are mystic psychiatrists of course :)

A 'good' psychiatrist must primarily have an understanding of the workings of their own minds - ie to have understood their own experiences, and why they perceive the world the way they do. To do this, they delve into their own psyche, and they come to understand the building blocks, they release their own emotional traumas before being able to help others. They also learn some theory and methodology, but this is empty and meaningless without a deep understanding of self. There are countless psychologists who are NOT qualified in this manner, although they may have the 'degree' that allows them to practice!

Once there is an understanding of one's own experience, it is possible to read people in a manner that allows glimpses into these building blocks of experience, which, coupled with the process of 'talk therapy', brings out the content of the 'subconscious' mind, such that it can now be looked at objectively and healing can take place.

But this is not 'mind-reading', it is about being skilled in picking up clues, reading the signs. Frankly, even if the mind could be read by the psychiatrist, this might not work. After all, the patient/subject is unclear in their own mind and has come to clear up the 'mess'. Therefore this also has to be patient work of investigation - there aren't any easy shortcuts :)