This doesn’t describe all experiences of trans people, but no analogy can. We are all so different. This is, however, a somewhat accurate representation, but slightly off. Most trans people were that gender their whole life, but needed time to realize. Lots of trans experiences are that they are a normal gender in their head, but their body is different. They never were a different gender, they just didn’t know who they really are.
A more accurate analogy would be that trans people are like apple users who realize android is better for them, not that they want to be an android user.
But I want to emphasize that your main point is correct - genders can just change.