We are the product of so much input beginning in childhood and we often need to fashion a narrative to understand ourselves as well as be able to explain that nature to others. Hence the phrase “born into the wrong body” was for some a way to express how they felt and an elegant description to explain it to people who had no concept of what being transgender meant.
Regardless of how each person feels, there is currently no perfectly conclusive scientific proof that we are born into the wrong physical body and it could perhaps be better expressed as being drawn to a gender identity which does not entirely align with our birth sex. This misalignment could vary from severe to mild and our method of grappling with it would change depending on the individual and their circumstances.
We all want to understand what makes us tick and having a catch phrase that encompasses our nature could be convenient but then we are far more complex creatures than that. How you express yourself and your gender identity and how you modify your body to reflect that, is entirely your business which is the way it should be. No one else has any right to comment on it.
Conversely you also have a right to not modify anything and still maintain an image of yourself as a “whole” person who is being true to themselves. There aren’t just two boxes to tick because that would be buying into a societal narrative that we were sold from the time we could understand language. Today, you are freer than ever to fashion your own idiom to explain yourself.
There is no straightforward way to describe how we feel to a person who is perfectly at ease with their birth sex and has never questioned it for a moment but, whatever language you use, rest assured that it will be good enough. Because to fully capture the depth and breadth of our full complexity as unique individuals would take up the equivalent of an entire book.