It is a logical fallacy to make a statement that a male person can 'feel' like a female person.
I don't know what it is like to 'feel transgender' (although I can say that I have suffered from gender dysphoria as a teenager). But that is because I am not a person who claims to be transgender.
Saying "And if you are claiming people can only feel like what they are, you can't possibly understand what it is like to feel transgender as you aren't transgender", doesn't hold together with your first statement, "You can say that they don't know what it is like to live with a female body but you cannot say they don't feel like a female person. You do not know how someone feels as you aren't them."
You are telling people that they simply cannot understand what another person 'feels', while claiming that the impossible is possible and that somehow a male person can 'feel' like a female person.
No. Those male people have conceptualised what a female person must 'feel' like, based on nothing but their own conclusions that have no grounding in material reality, and they have categorised those 'feelings' as being female.
I can most confidently say that what those male people 'feel' is not 'female' because the only possible way to 'feel' female is to have a female body and to negotiate interactions having that female body.
Just because I don't know how that male person 'feels', does not mean that I don't fully understand why that male person cannot 'feel' like a female person. I don't know how they feel, this I agree with, but there is no possibility on earth that that male person 'feels' what it is like to be 'female'. They only can feel what it is like to navigate life in their body, which is male and remains male for their entire life.