Is accepted as a reason as to why you might be afraid of VB. It's not proven to mean you will have a difficult birth but my consultant was understanding when I explained it as one of the things that put me off.
There is no evidence that a family history of a difficult birth, means you will also have one.
HOWEVER
It is fair and acceptable to say, that although you know this to be the case, you still can't come to terms with that in your head. What you know true rationally and logically is still not removing your emotional worries and fears about what could happen because you have someone close to you who has found it difficult and this has a disproportionate influence on your thinking. This is causing you anxiety and stress in its own right.
Its a subtle but important difference which makes it a fair argument.
Fear and phobias by their nature are very emotional, and are difficult to negate with logic and reason. If you can demonstrate you know the difference, it puts you into a position where they can look at other ways to deal with that rather than just giving you information or merely saying you are wrong.
If you can articulate what part of the family history of difficult births is the thing troubling you the most, they might offer a way to try and cope better, or try and manage a natural birth better. If you say X risk associated with a VB is something you are not comfortable with, but you are more comfortable with Y risk associated with a CS then again you are demonstrating an understanding of risk and something they can work on managing.
Yes, an ELCS might ultimately be the best way to deal with it, but equally its also about pinning down exactly what element of giving birth is giving you most cause for concern and then giving you a range of options to deal with that.
I have to say, I found the process of breaking down fears, very useful in its own right, as it helped me to understand the fear. Just being able to articulate and rationalise it, even if my irrational fear won out made me feel a bit more in control of the situation. I felt 'stupid' at first, but other people saying, no you are not stupid, how you feel is understandable given your knowledge and experience was important in a variety of ways. It helped to build trust and respect on both sides.
Its very much about framing and opening communication channels, particularly ones you didn't think possible when you start out.
Which is why I do say that, just saying 'no' without listening is just about the worst thing that could happen. Even if that is eventually the case, then there has to be a process of listening, communicating, exploring options and a explantion which answers your concerns to the best possible and most comprehensive standard. The eventual outcome has to be about whats in your best interest in the long term.