Maybe that is all you are dwelling on, so it seems to be taking up more time than it really is. This is something that the character was either repressing or thought she couldn't be, so the way she is coming out about it is actually more true to life than if she just told everyone and got a a smile and a "good for you" or the opposite, and then carried on their lives as though nothing had happened. We didn't see Kara cone out and tell everyone that she is Supergirl and from Krypton for the same reasons.