Thank you for trusting your question to JA today. I am a licensed attorney with over a decade of law practice and over 20 years of experience in the legal field. I’m happy to be of assistance.
What you have to understand about separations is that they are done at the discretion of your commander. There is no method of compelling separation short of testing positive for a drug, which requires a commander to initiate separation.
Otherwise, the commander can only have separation recommended to them. The common methods are to go through medical, noting your depression, and using the doctors to recommend separation based on not being a good military fit. One your facts, you can use the medical staff and also approach the chaplain's office to express your depression and desire to get out because of it.
All medical and the chaplain can do though is make a recommendation to your commander which your commander can accept or reject.
I wish I could tell you differently here. I would prefer the military be entirely volunteer, but given the near constant state of our combat operations over the last few decades, all the old "loop holes" for separation have been closed. They simply don't apply any more, legally speaking.
If you have any further questions, please let me know. I invite follow up questions, so use REPLY for those. If you have no further questions then good luck going forward and please do not forget to rate my service with a top-three rating so that I receive credit for working with you today. Please rate me based on my service and not on your satisfaction with the law, which I am not in control of and I am just reporting to you. Also, feel free to request me in the future, if you have questions concerning a different matter.