People can think of themselves as anything they want. But forcing others to adhere to their demands and be addressed as something that denies basic biology isn't reasonable.
But that's it- it doesn't deny basic biology, as ultimately, psychology is part of biology via bio-chemistry.
You are under the false impression that one fine day, a guy wakes up and thinks 'I wanna be called a girl', or vice versa.
No. There is extensive scientific evidence, that some of us feel like the other gender, as in the way they see themselves.
Its similar to being gay.
And there is nothing unnatural about either of these (though cross-gender is impossible to verify if you cannot communicate with said animal directly, homosexuality is a natural thing- its found in tons and tons of species, even in our closest species (the apes).
So the entire point is, if someone feels like they are a woman but looks like a man (or vice versa), whats the big deal about simply addressing them as they want ?
This is basic discrimination actually. Think about it- when we meet a guy for the first time and he says ' call me mr smith', do you go ' who the eff are you to force the mr on me, Smithy-boy ?' or do you go 'sure, mr smith' ?
So if a dude says to you 'call me Ms Sally please', you are denying the same basic courtesy you are according to cis-gendered people.
Its their identity. And they have as much of a right to it as you have to your concept of Identity- for eg, being muslim or being Pakistani or whatever.
Again,basic humanity is missing from the whole right-wing argument. Its not a matter of being bleeding heart, it takes a grand total of 2 seconds in most people's lives to address a person as a mr or miss most of the time anyways.