Does the Mexican consulate have the right to deny me citizenship even?
You need an attorney to defend your rights. The Mexican Constitution Art. 30 says that anyone with one parent born in Mexico has Mexican nationality by birth. It does not have restrictions. A good attorney can verify your fathers birth in Mexico and your nationality cannot be denied. This is not something to be decided by a Consular employee, it is considered a human right in the Mexican Constitution. You can verify your nationality and take action against this Consulate employee.