What is it with services now separating username and password fields?

Back in the old times, on the sites I log in regularly, my browser filled in both username and password. I clicked "Log in" once, and I was set to go.

But no more. Now it's all first a username, then a password. From what I saw, Apple started this many years ago, but now this bother really spread. And it's not like I can just double-click on the same screen area, oh no. Animations make sure that I have to wait several hundred milliseconds before the password field is there, and depending on the site, I even have to select from my browser, which login I want to use, twice!

Why, oh why?

All my screens are really big enough to display 2 text fields. What are arguments for this behavior? I don't see any.