It is not their place to tell YOU stories about yourself that are obviously not true. It is not your place to take on stories they have themselves about you
If it's what you want, then they have the wrong 'story' about you and you don't have to take it on.
They may not support you, but you are the birthing woman and you don't need their permission to seek the birth you want, you just WANT their support. Sure, it's nicer when you have their support and sometimes you just have to work a little harder to get there under your own steam. Looks like you'll be taking all the credit for yourself when the birth happens according to YOUR values.
Please, keep telling yourself your own positive 'story' - it's far more useful to you and it becomes easier to filter out the negativity
You're making a wise choice