I'll take a shot.
>> critical thinking
> Why can't the student's knowledge of logical fallacies be tested?
There's far more to critical thinking than logical fallacies: understanding what someone is saying, cutting through the verbiage to the actual argument (assuming there is one!), questioning the assumptions (false assumptions ---> false results even if your logic is perfect), recognizing ad hominem arguments, understanding statistics (although perhaps you're including statistics in logic). Some of that can be tested, I imagine, but it's hard. You have to devise tests that can be computer graded (given the size of the testing population), and then validate the answers. Organizations like the ETS have, I believe, spent lots of time and money on that. I'm not familiar with the literature, so I'm not prepared to say it _can't_ be tested, but I wouldn't be surprised to find it's _not_ tested much.
>> Some say creativity can in fact be tested.
And some say it can't (http://www.experts123.com/q/can-creativity-be-tested.html). Now I have no idea whether the link I just gave is "right", but I don't know about the one you gave either. I suspect the problem is rather one of validating that tests of creativity predict something useful in the real world. One could say the same about most any other test, but I would _guess_ that it's more true of "creativity" than it is for most other tests. (Which may be the answer to the question you're responding to: we don't test for things when we can't ensure matter.)
> or learning skills.
>> Learning skills such as critical thinking and creativity? (See above.)
Or the ability to see other points of view than your own, or to pay attention, or to synthesize different fields (math and physics, for example), or to stay awake in class or when reading the textbook, or to remember after the final exam, or to use the information you've been given in the class to explain real world events, or to arrange a pile of data into a predictive "theory" (more useful for some studies than others--in my own experience, more useful for inorganic or organic chemistry than for biochemistry, where afaict the facts might have been any number of different ways, but God chose one--perhaps for reasons known to Him, but not revealed to me).
In general, I think the AC you're responding to has a point: we tend to test for things that are easy to test for, and hope that they're important. Sort of the keys-under-the-lamppost problem. That said, there are plenty of proposals out there--like the creativity tests your link mentions--for testing other things. The questions are, 1) are they reproducible? 2) do they matter in the real world? and 3) can they be improved (by teaching or otherwise), or are they purely genetic (for example)?
And I hasten to add that there's a huge literature out there on this, about which I know nothing.