They are not trying to destroy or erase anything, they are trying to be seen, accepted and loved by who they always were on the inside. Trans people are not a third gender unless they, as individuals, say so, they can be female, male or whatever else they feel like.

I'm trying to come up with an analogy that works but it's hard. The bottom line is: people's identities should never be defined by others and ought to be respected.

Humans mainly have two biological sexes - male and female. Gender evolved around those concepts and is a set of behaviors, expectations and norms that presents two polar opposites - men and women -, however some people fall in between those two opposites.

There are people who identify with both male and female or no gender at all, but that has nothing to do with being transgender, same way being intersex has nothing to do with it either. Those people would be what is usually culturally and historically seen as a "third gender", among for example the native american people or indian culture, and in modern western countries those people would usually be non-binary or genderqueer.

Trans people are not necessarily confused or in-between genders, they can be men or women (or non-binary), and it is not anyone else's place to dictate how they should be segregated for having been born with a more complicated life-path. Gender is how society sees you. People should have the right to be seen how they are on the inside.