But if that is happening, presumably it shows up in your reasoning and can be critiqued.
Logical thinking is one tool for developing self-awareness but not a necessary one.
For myself, I’m bipolar. Self-awareness is critical to keeping myself grounded and processing extreme emotions safely. Many people have told me I am an expert at this and I still fall into this trap again and again. I just eventually realize it.
I know many smart people who are blind or willfully ignorant of their own assumptions. This includes a number of vocal advocates of theology, philosophy, and rationality.