can you please explain what makes (A)incomprehensible incorrect and (B)tangential correct

Greene’s discussion of the nuances of particle physics, though seemingly __________, actually serves a purpose

Actually serves is the clue to say: apparently, the discussion or what the author pointed out was out of scope but in the end, it had a purpose

Indeed, without this background, the reader would be unable to ________________ the significance of the evidence presented later in the book.

So appreciate what was in the book

Hope now is more clear

Regards

For the first blank it is tangential, because it mentions that those information serves a purpose.
The second, we are looking for word that close to discern or to understand.
obstruct ==> to block (no)
synthesize ==> to mix (no)
appreciate ==> if you appreciate something you know about it (yes).

why not incomprehensible in the first blank it seems to be the best fit here?

The argument at a glance did seem out of scope but indeed it was on purpose.

See my explanation above also.

A is completely out of scope

Regards

Blank 1:

Incomprehensible - lack of understanding. This seems a common usage to speeches that are difficult to comprehend/understand. However in this context, it is "tangential" which implies that the discussion is not directly relevant to the main theme (significance of evidence - mentioned in line 2).

Blank 2:
Even though the discussion did not directly address the topic (it was tangential), without this tangential background discussion, the reader would not be able to "appreciate" the significance of evidence presented.

Incomprehensible is very very tempting, however it does not fit with the idea that the sentence is trying to convey. One cannot appreciate the idea of something that was incomprehensible.