I didn't drop out, but I flunked out of grad school. (severe depression).

After flopping around in bed for three months afterwards, i got myself a job. I figured out what I truly wanted to do in life. I made the plan, and I have been a Neonatal ICU nurse for about 5 years now.

Ask your kid why they want to drop out. Give them some time to get a job and then move out. But most of all, be supportive. The rift this created with my family still affects us 11 years later.