Hi ratperson!
Soo... gender categories are the best thing people have been able to come up with (so far!) to describe the irreducible complexity of human gendered experience. They're imperfect, and sometimes feel difficult to understand and navigate. But in general, cisgendered people are understood to perform a gender that is the same as the one they were assigned at birth. Trans* on the other hand encapsulates many different expressions of non-normative gender, depending on the individual: those who transgress the gender binary by choosing to enact a gender different than the one they were assigned at birth, or those who transcend gender, and don't identify as either male or female. Basically, cis and trans are "opposite"-- although this binary might rub some people the wrong way-- and trans*
may include people who identify as gender-queer, or otherwise non-binary; although some gender-queer, gender-fluid, or non-binary peeps may not group themselves under trans*. It's really a matter of self-definition and the power of name-claiming. You probably received a hostile response (not that it was warranted, per se) because trans* people may be wary of those who have cisgendered privilege (ie, people with normative gender/sex experiences or appearance) infringing upon a personal and political safe space for trans* folks and mis-using or appropriating certain terms. I don't at all mean to suggest you were doing this, but in their everyday lives trans* people face threats of violence, humiliation, exclusion, etc. so that's where some defensiveness might come from.
Basically, what is "possible" is culturally constructed through categories recognized and affirmed in our society. These categories are constantly adapted and negotiated, and most importantly are the result of power dynamics that privilege some and oppress others--for example, cis people are privileged and viewed as full gendered subjects, and people who do not conform to varying degrees face various kinds of oppression, and may claim names and identities to assert their personhood and social intelligibility in the context of social forces that dehumanize them.
I hope this helps... If it seems confusing and wishy-washy, it's because issues of identity
are confusing and wishy-washy. Anyway, here's some more info from Scarleteen if you're interested:
Genderpalooza! A Sex & Gender Primer
I'd also recommend reading some queer theory if you have the time (If you really want to have your mind blown, read some Judith Butler)! There are so many perspectives out there to consider, and the more you read and learn, the more rich and nuanced your understanding of gender (and yourself!) will become.