It is not just needles some people are petrified of having their BP taken or other tests done and the Doctor finding something wrong.
In the case of pilots it could be fear of loosing a licence and hence job or income.
In non pilots fear of loosing their health or fear that they have something wrong and the doctor confirming those buried fears.
Many of these fears go back to childhood. So needles, a blood pressure cuff, an ECG even a hospital smell can drive the fear of god into many.
Pace