I don't know if she has to be furious given the scope of his secret, it comes down to the age old reason of secret super identities, i.e. protecting those close to them and trying to have a normal life. I think Lois can understand that ( and hopefully they talked about it after the big reveal).
Exactly. What that scope means is that Superman has a greater responsibility to the world (after deciding to work for it), and that cancels out any purely subjective notion of another person's "right" to be told about his true identity. His most personal and protected secrets only becomes the business of another when he decides its their business, no matter how long that takes.
People are entitled to their secrets. Clark should feel like he can tell or not tell someone something very personal whenever he feels most comfortable. Also the idea of people knowing his secret being in danger is still a danger so their is also a added level responsibility of whether or not you should put this burden of knowing the truth on someone. Especially complicated when you love that person.
Some continue to ignore the danger of a superhero's life on civilians, all because they want everyone to be "in" on that most dangerous of secrets (right out of the gates), which--as comic book history has laid out time and again--has taken the darkest of turns.