newhorsemom, I have a horse, Walka, that to say he is needle shy is a HUGE understatement. I could wonder and suppose why but the reality is he does. What we've done, and by we I mean my vet and myself as it's a team effort, is this... first, I have mimiced all the actions that the vet does. Pinch the v area on the neck used a syringe and poked though not real hard ect... weeks ahead in preparation. No problems.
Now it's vet day. I have a very understanding and calm vet and he over time, and it has taken just that, worked with Walka and his fears by talking matter of factly and business as usual and will circle him and give him his shots. At first it was really scary, but Walka was trying to get away, not hurt anyone. Now, this last season, my big brave boy (yes I'm being sarcastic) stood still, ram rod still, and took it like a "man". And my vet had to come back for boosters that season too.
It has taken a few years to get here but it looks hopeful. If your vet has any savy, he or she will see that it is a fear issue not an attitude issue. The vet's demeanor will either excellerate or calm the situation.
I cannot hold the lead rope for my vet with Walka, because Walka feeds off my anxiety. That is how sensitive some of these horses are.
Good luck, hope you find a horse savy vet and don't get discouraged.