Denied Delta Amex Gold SkyMiles

I called the reconsideration line and was told that I have too many recently opened credit cards, yet I only opened one last year in September. I am a part time college student with a part time job (with low income, of course), but I selected employed instead of student on the application and even explained that on the phone if it even matters. Couldn't get the denial overturned, but I was told to reapply in a month and switch my status to student. My credit score is in the very good range, and my utilization is currently at 4%. Is selecting student that big of a game changer for approval?