Sentence Correction

Dear all .. in the folowing question:

Unlike computer skills or other technical skills, there is a disinclination on the part of many people to
recognize the degree to which their analytical skills are weak.
(A) Unlike computer skills or other technical skills, there is a disinclination on the part of many people to
recognize the degree to which their analytical skills are weak.
(B) Unlike computer skills or other technical skills, which they admit they lack, many people are disinclined
to recognize that their analytical skills are weak.
(C) Unlike computer skills or other technical skills, analytical skills bring out a disinclination in many people
to recognize that they are weak to a degree.
(D) Many people, willing to admit that they lack computer skills or other technical skills, are disinclined to
recognize that their analytical skills are weak.
(E) Many people have a disinclination to recognize the weakness of their analytical skills while willing to
admit their lack of computer skills or other technical skills.


I understand the answer will be between D and E. But why D between these two?
Answer explaination in OG says "In E, have a disinclination... while willing is grammatically incomplete"
I am not able to understand why it is gramatically incorrect. Somebody, please explain.

Thanks in advance

while is used to introduce a clause but in this sentence it is introducing a phrase

Remember on GMAT While and Although must be followed by a cluase

I guess E option is quite wordy and awkward..GMAT prefers better writing style if everything is correct grammatically and D is more concise

Thanks ppl for replying ...