From page 37:

There are three types of improvements you can select for your character:

• Characteristic Advance
• Rank Increase
• Skill or Talent Advance

From page 38:

Ranks

...You may sometimes find yourself eligible for two or more Ranks...

Gaining Ranks

Characters Automatically gain Ranks by spending xp....

So you can choose to increase your Rank. Except your Rank is just a measure of how much xp you've spent, so you can't really choose to increase it. It automatically increases once you've spent a certain amount of xp on Characteristic/Skill/Talent Advances.

Also, looking at the career paths, it doesn't appear that there is ever an opportunity to "make a choice between the Ranks available to you". The paths don't fork, there's only Rank 1, followed by Rank 2, Rank 3, Rank 4, etc, which are all automatically gained when you spend a fixed amount of xp.

What am I missing?

When is there ever an option to increase your rank (instead of characteristic/skill/talent Advance)?

When is there ever a need to choose between two different Ranks?

Lots of stuff in Rogue Trader is copied directly from Dark Heresy, which does have branching rank options. This is one of the things that should have been changed, but slipped through. Or you could argue that they were just keeping the option to make branching ranks in a future release. Either way, just ignore it.

Alternative ranks do exist in Into The Storm, but they come with their own rules.

The branching rank paths really do not factor in unfortunatly as been said. There are alternate ranks in Into the Storm which sometimes take the place of a certain rank and a up coming supplament may have more rules for this subject. Also they may be there for any home brewed ranks or DH imports.

Thanks for the clarification. I was going bonkers back and forth though the book trying to figure this out.