Here is the hard-and-fast grammatical pattern taken from the language itself as a living organism (maybe that is going too far) that shows that whereas is not a subordinating conjunction.
- The boys played tennis and the girls played volleyball.
Everyone (I hope) will agree that the word and is a coordinating conjunction because the bits on either side of it, but not including it, can stand on their own. Can they stand on their own? Yes? Well, then the word and is what allows that.
You can substitute any of the so-called coordinating conjunctions there, remove them and you create two stand-alone utterances that are independent clauses. That is way to see how two independent clauses may be joined.
Now, if you use whereas instead of and, the same is true as regards the sentence above.
Now take the OP's sentence:
- I am disinclined to recognize my weak mathematical skills, whereas willing to admit my lack of English skills.
If you want to introduce a whereas in that sentence, you need to do this:
I am not willing to recognize my weak mathematical skills whereas I am willing to admit my lack of English skills. OR
I am disinclined to recognize my weak mathematical skills whereas I am willing to admit my lack of English skills.
I am disinclined to recognize my weak mathematical skills whereas I am not disinclined to admit my lack of English skills. or: not so disinclined as regards my English skills.
Most grammars/grammarians do classify the word whereas as a
subordinating conjunction where an independent clause is joined to an
dependent one. However, all you need to do is see whereas used in texts,to see that the clauses used with it are not "subordinate to one another."
The word whereas in sentences contrasting "equal" utterances (subject, verb and predicate) plays a coordination role and not a subordination role. This can be seen by substituting any of the well-known coordinators such as but or yet where two clauses are coordinated, which are called coordinating words, and there is no "subordination". The kind of logic one finds with subordinating conjunctions is not the actual logic of the use of whereas (in its non-time meanings).
Here is a traditional explanation of a subordinating conjunctions, and it's pretty good too: subordinating conjunctions