You would have to choose #1 , because #2 contains the diparaged construction "the reason why".
However, neither #1 nor #2 is a good rephrasing of the incorrect example.
For one thing, "what is the reason" was changed to "is this the reason", which changes the meaning.
For another thing, "neglecting doing" is awkward. Of course, simply taking out "doing", as user8399 suggests, changes the meaning. "Neglecting to do..." would be better.
For another, If you treat "neglecting" as a noun, it should be your neglecting. . . " rather than you neglecting. . ."
So really, the correct answer is that neither #1 nor #2 is a good rephrasing.
Feel free to tell your teacher this; and that the question should be thrown out (not counted), because it was so badly written; and that you deserve extra credit for this analysis, not a downcheck for whichever answer you chose.