The believer says that only God knows one's intent or how good or bad one is inside.
To claim that only God sees the soul is to draw a boundary. Humans, it implies, see surfaces: behavior, speech, reputation. God alone sees essence. That can be a way of silencing those who judge or who are offering even constructive criticism.
Tacitly, it means that if God were to delegate the ability and authority to another to judge one that would would defy.
Saying "Only God sees my soul - only he can judge me" can be a response to the fear that I do see what I think is my soul myself. I want to be in denial and protect my denial. I fear others see it too which is why I may go to big lengths to protect my artificial image of myself.
So it works less as a statement of faith alone and more as a psychological
and existential shield. It is a way of managing the anxiety that comes
from partial self-knowledge, denial, and the terrifying possibility of being
seen by others more clearly than we see ourselves.
It is sly for it appears, on the surface, to be an expression of humility or
faith.
It can imply that God sees how wonderful you are and how most of the harm you
did was done without malicious intent - that God is so wrapped up in love for
you that he downplays your evil side.
You do not know God personally - so you are filling in the unknown with your own ideas and feelings about him. He is too much about what you want him to be - a sort of extension of yourself. So a loop appears. God will tend to affirm or downplay the bad things you are and do. It is no wonder you want his judgement and for him alone to judge.
Another danger is that you want God who supposedly makes your sins as white as snow and literally forgets the past to judge you as forgiven.
God's judging is put into the distant future. If you do evil and one bad thing happens after another, to say "God will judge" ignores if he is judging you now.