Surgeons say I don't qualify for FUE hair transplant, is it the hair density, or bold areas that couldn't be covered by donor?

Your surgeon had the luxury of examining you to give you a DIAGNOSIS and RECOMMENDATION.This would pure guess work as to why your surgeon told you that you don't qualify for a FUE surgery.You need to ask "WHY" to the doctor you saw.

This can't be definitively answered unless there has been an individual examination. And so I wouldn't comment on wether your surgeon was right or not in declining you on basis of candidacy. However I can elaborate a little on what we consider when we decide upon a patient's eligibility.
We definitely proceed with caution before we approve candidates who are under the age of 18. In rare cases, people that young do want this procedure and they will be carefully vetted before being approved, if they are approved at all. So, age is a factor. 
Another factor is the general health of the patient. For example, a surgeon will look at medical history, current health conditions (if any) and then decide if it’s safe to perform the procedure. In some cases, a candidate may need to resolve health issues prior to being approved for the surgery. 
Also, patients should have immune systems which are strong enough to allow them to heal properly after their operations.
Doctors prefer to perform hair transplants on patients who live healthy lifestyles. So, following a healthy diet, getting moderate exercise and practicing stress management will boost your odds of getting the “ok” for this type of surgery. 
A surgeon will also look at your degree of hair loss and how much donor hair you have available.
These are some variables. If you really want to make sure about your candidacy, you could book another consultation with another cosmetic surgeon in your city. Just make sure you chose a skilled, experienced, certified and well rated surgeon. 
This will be the best way to see if you’re a viable candidate for this type of procedure, as every patient is different. Only a surgeon can tell if this procedure is right for you.

There are some relative contraindications and some absolute for any type of surgery. FUE can be done in most of the people. But there are some surgeons who do not operate if the person is having a very large area of baldness, retrograde alopecia, curly hair, etc. SO, without knowing your history and your pictures, it is unrealistic comment about your case.