Kosher Wine

I have asked this question and have not had a satisfactory answer
from anyone. If grapes (or apples, or any other fruit) are kosher,
and if grapes are left to ferment, with nothing added and become wine, why isn’t the wine kosher? I have been told that the people who make the wine are not Jews and therefore, the finished product is not kosher. That, in my opinion is nonsense. If cows are kosher, and the milk that comes from them is kosher, does this mean that if the farmer is not a Jew, the milk is not kosher?
There are about 60,000 Jews in the Dallas area who are not affiliated with a synagogue (I am one of them) and answers like this are only causing them (and me) to just give up on Judaism as the answers to common questions like this are meaningless. I am very confused and frustrated.