Fear of Hurting dissapointing or hurting parents.
Praise be to Allah who has guided you to Islam
Allah has blessed you immensely by choosing you to become Muslim. I ask Allah for you to be the cause of them also entering into Islam.
When a daughter (or son) loves her parents she wants what is good for them. Since Allah has blessed you with Islam. You should want this (Islam) for your parents too. No child who loves their parents would want them die as non Muslims and to be tortured firstly in the grave and then the hellfire for eternity.
Hurting their feelings is nothing compared to the pain they would receive in Jahanum (hell) in the next world.
In the next world they will say you were our daughter and we did so much for you but you did not tell us about Islam.
Allah has also enjoined on you to call your family to Islam.
"And warn your tribe (O Muhammad) of near kindred"
So they are the first one's you should call to Islam as they take
If a person fears that their parents will kill them for speaking to them about Islam then obviously you will not be able to preach to them until you are in a safe place.