I have recently discovered this *flaw* as well. I say flaw and not bug because I do not know if it is intentional or not on the part of Maxis.
Within my sim family, I have completed all careers, all branches, but, of course, I want some sims to complete all careers and all branches on their own.
I first discovered that once you choose a career branch, you can't go back and try the other one, when I tried to re-join the Culinary Career, intending to become a Mixologist this time, in order to complete the Mixology Aspiration, just as ams12277 mentioned. That seems to be a common way of running into this issue.
That sim of mine was first a Tech Guru-Start Up Entrepreneur Branch, then in the Culinary Career-Chef Branch, then Criminal-Boss Branch, then a Painter-Patron of the Arts Branch. When I went to choose his fifth career, I had already taken into account which aspirations he had yet to complete, which weren't many. I still needed to join the Mixology Branch of the Culinary Career Track in order to complete the Master Mixologist Aspiration.
So, when I went to choose my fifth career, I noticed some odd things. The usually careers were listed differently. Any career that I had previously completed to level 10 had a new name. Instead of "Culinary, "Tech Guru," "Criminal," and "Painter," I was given the choices: "Chef," "Start Up Entrepreneur," "Boss Branch," and Patron of the Arts."
In other words, if you go to rejoin a career that you have already completed, you will actually be joining that career at "Level 6" in the branch that you previously chose.
Furthermore, when you join that career, it will not actually be called Level 6. For instance, I joined the "Chef" career, and I am now a "Level 1 Chef," with the title of "Head Caterer." "Head Caterer" is really the Level 6 job title of someone in the Culinary Career, after they choose the Chef Branch.
To complicate things further...
I joined the "Chef Career" having not yet completed the "Master Chef" Aspiration. I am in Step 2/4. One criteria for completion of that step is "Reach Level 5 in the Culinary Career." Well, since I am considered a "Level 1 Chef," I only show credit for completing 1 of 5 levels of the Culinary Career itself. I will have to wait until I reach "Level 5" of the "Chef" career, which is actually Level 10 of the Culinary Career, in order to get credit for reaching Level 5 of the Culinary Career.
Unfortunately, at this point, it looks like this sim will not ever be able to complete the Master Mixologist Aspiration.
For Reference:
There are 4 Aspirations that have requirements related to career promotion and only one specifies a branch of that career.
1. Public Enemy:
For Step 3, you must reach Level 4 of the Criminal Career.
For Step 4, you must reach Level 8 of the Criminal Career, but it does not specify which branch. *However, given my experience, you must try to complete this step on your first time around in the Criminal Career because, as I mentioned above, when you join a career for the second time, it starts at Level 6, but counts it as Level 1, so during your second time in any career, the highest Career Level you can attain (or get credit for attaining) is Level 5.
2. Master Chef
For Step 3, you must reach Level 5 of the Culinary Career.
3. Master Mixology
For Step 4, you must join the Mixology Branch of the Culinary Career.
4. Computer Whiz
For Step 3, you must reach Level 2 of the Tech Guru Career.
For Step 4, you must reach Level 5 of the Tech Guru Career.
**So basically, if you want your sim to complete all aspirations, he or she must join the Mixology Branch of the Culinary Career. He or she much also join the Tech Guru and Criminal Careers, but it does not matter which branch they choose.