I thought I must offer at least one reason to have a multiple page login.
The only real advantage (disadvantage in most cases) of using multiple pages, instead of one, is that the user is provided an expected flow they must carry out. This could help with sites that don't have a conventional flow or sites where the expected use case is a step-by-step process. One tactic used by sites where being a user requires payment is that it splits up content that needs to be entered to make the user feel committed in continuing.
I think there is at least one example of where the two page log-in makes sense.
Sites where the average user is not the average computer user, but instead is only on their computer when forced. Also, most users only sign in once or maybe a couple times and never need to log in again. This case is becoming less and less common.
I happen to mention this because I used to be phone support for a company that frequently had older men or women trying to figure out what they needed to do to get product(x) working for their child again. They had to enter an email and password at some point, but then didn't need it again until much later.
Quick overview on the User
This kind of user will log-in only once-in-a-great-while to do one particular task. When they get to the main page, they may become instantly lost with all the information (even if it doesn't seem like that much). They just want to log in, do something, and get out. Simplicity is this user's friend and the less options they have, the better. If they do have choices where they are not sure what to do, they try to go with what seems the "more common" choice, which could be determined by how much screen size it has or simply which option they saw first.
Comparison of Single-Page vs Multi-Page for above User
Single Page: First time user lands on entry page. Hopefully, the log-in/register portion is highly visible for this user. They may not notice the register portion or wonder if they already registered. After all, they did register on that one site a long time ago. They proceed to guess at usernames/passwords. Eventually, they try all known combinations and realize they need to register, or they finally notice the register option.
Multi Page: First time user lands on entry page. This time, the website asks for their username. (Which, again, should be highly visible). They enter their email and the website tells them the next step. In this case that step is to register, and the user has already filled out the email.
I didn't really mean to write a paper, but it was important to note that the expected use and target audience of your site have a large influence on design. It could be your boss expects the kind of use or audience mentioned above, or foresees a large number of users not knowing their username because of some other system which may be similarly named or connected. Maybe your boss himself is one who always forgets which username he used, or maybe he hasn't considered the fact that you could tell him whether the username is correct on the first page. I believe in most cases for today's world, a single page for signing in should be sufficient and desirable. There are some cases otherwise, however.