You had a secret. That isn’t surprising because the Wayne family is full of secrets and fake personalities, but this was a different situation. You were lying to your family, not with them, and it’s impressive how long it’s lasted.
The family was made of vigilantes that protected Gotham, but you didn’t do that, or so they thought. They believed that you were normal and innocent, but they’re wrong.
On a field trip, you got bit by a radioactive spider and ended up developing spider-like powers overnight. You got scared to tell your family and ended up making yourself a suit, sneaking out around the same time they do to explore the streets as a spider.
Your family, especially Bruce, keeps on complaining about this meta while your brothers along with Cass and Steph don’t seem to be freaking out. They’re completely clueless, but nothing good lasts.