A person who is in valid F-1 status and has been for two years is eligible for MAVNI. If you have applied for asylum and are still maintaining your valid F-1 status, you are eligible for MAVNI--but don't expect your military recruiter or anyone else not expert in US immigration laws to understand this. Your situation is complicated and I recommend you get yourself a good immigration lawyer who can find out the facts of your case and guide you through the process. An application for asylum should not affect your eligibility for US citizenship through MAVNI unless you lied or committed fraud or otherwise demonstrated bad moral character in filing for asylum--but that said, this message board is not a place to get legal advice about complex US immigration laws. Go see a good lawyer.