There’s nothing wrong with the term itself, except that it’s out-of-date. The term was deprecated when DSM-V was published May 18, 2013, in recognition that issues stemming from incongruence between the gender assigned at birth and the gender experienced are not disorders, but rather, that it is a condition. The proper term is now Gender Dysphoria.
Unfortunately, the current version of ICD (10) still has a code for Gender Identity Disorder (F64.*), but the recently ratified and soon-to-come-into-use version 11 updates the language to “Gender Incongruence” and moves it under the section for “Conditions related to sexual health”.
In other words, the misconception that transgender people are suffering a mental disorder simply because they are transgender is being corrected in the references that medical and mental health professionals use. Hopefully that same understanding will also soon come to the general public.
There’s nothing wrong with being proud that you’re cisgender, just like there’s nothing wrong with being proud of being tall. Just don’t be a jerk about it.
Being cisgender means you are part of a majority — one which you have done nothing to be a part of. It means you have had an easier life. It means that you haven’t had to face stigma, ridicule, and discrimination for having your gender not align with the one you were assigned at birth.
It does not mean that you are somehow superior to people who aren’t cisgender, and it doesn’t mean that you get to ignore or mistreat those who aren’t cisgender.
Just like being tall, you’ve done nothing to acquire that particular trait — it just happened to work out that way.
So please, be proud of being cisgender. It’s great when people feel good about themselves! Just don’t be a jerk about it.