I'm applying for a PhD in neuroscience and I've recently finished writing my SOP and supplementary essay. My supplementary essay asked me to respond to the prompt "Please tell us about an incident in your research where you experienced failure. Include what you did about it and what you learned from the experience." I wrote about how due to my social anxiety I failed to reach out for help in preparing for graduate school, leading to a delay in attending graduate school. I wrote about how I corrected my behavior to no longer respond to anxiety with avoidance. Most of the essay focuses on what I did to correct my behavior and my talk of mental health is kept fairly minimal. I asked the admissions whether it was okay to write about a personal difficulty I overcame throughout my academic career instead of a technical failure in the research process, and they said this was fine. However, when I showed my essay to my academic advisor he said I should avoid mentioning mental health and therapy as it might scare off the admissions committee. The specific lines he had a problem with were as follows:
"However, towards graduation I became preoccupied with moving away from my parents instead of preparing for graduate school. This was despite the fact that they offered to pay for my graduate education on the condition that I stay. I later learned, through working with my therapist, that I was attempting to escape an abusive environment."
I feel as though these lines are very important to contextualizing the situation. Would a line like this really scare off admissions?