No person can understand who something 'feels' that is not their personal experience.
And no male person can ever experience life as a woman. They can only ever experience life as a male person who believes they are a woman. (or, who 'understands' their experience as being a 'woman's'.
Even when they 'act' like a woman, they are acting as they believe a 'woman' should act. Even if they are treated 'as a woman' by some people, they are being treated as a 'male who presents as a woman and believes they are a woman'. Because their every reaction is based on that. Not on them being female in any way.
Even when they have extreme body modifications, it is to be their own concept of what a female looks like to them. It is not what a female is.
How can it be?
The only way a person can experience life as a woman, is to have a female body, formed around the production of large gametes, even if it doesn't produce those and to navigate their life based on the decisions they and society makes that revolve around them having that body.
A male can conceptualise what it might be like to be a female, but that is all it ever is - their concept of being female.
They may do it because they don't feel they fit into how they conceptualise how a male person interacts with the world (ie. their own stereotypes around being male) or they do it because they want to be seen as a female (using their own stereotypes of how a female navigates life). It really doesn't matter though. Their motivation is irrelevant to the outcome. And I consider the outcome can only be described as misogyny.
Which is that they will always be just a male who believes they are something they are objectively not.
How can the material reality be any different? This is why someone's gender is only based on someone's philosophical belief. And philosophical beliefs are fine for people to hold, but not one person in the UK has to comply with another's philosophical belief.
The logic cannot be any different than that I am afraid.
Sure a male person might ‘feel’ different than they label a stereotypical male person’s interaction with the world might be, but it is only based on that individual’s labelling behaviours and interactions using their sexist understanding of the world. All they are really doing is incorrectly labelling their own male perspective and interactions because they reject what they, personally, perceive as what being male means.
There is no possible way for someone to have the ‘wrong body’. They can only have the body they don’t want to have.