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.
Your example sentence
Make sure you spread the ointment into the skin
is grammatically correct and understandable with the meaning
Apply the ointment so that it penetrates the skin
however the phrasing may be found awkward by native speakers. The awkwardness arises from the use of spread...into.
Skin is a surface which things are usually placed on, over, or through and sometimes into
The wind on his skin made him feel cold
She poured water over her skin to wash it
The splinter pierced through his skin
The injection was made into the second layer of skin
Ointment can be applied over skin and then allowed to penetrate into the skin due to the latter's permeability.
Make sure to spread the ointment over your skin until it is absorbed
may convey the message you want with less awkwardness
Best Answer
Short answer: a lot of native speakers use organize for. A search of authentic examples suggests that its usage is 'correct', even though some readers (such as myself, a native speaker) may not be thrilled with it.
Longer answer:
I do not particularly like organize for. But when I search Google Books, it brings up a lot of authentic uses. See my search results. Sometimes Google results can be deceptive, but even as far as Page 6 of the results show authentic uses by native speakers.
Organize for seems to be used along the lines of prepare for. The latter is a collocation that is time tested as 'correct'. Language is always changing, and although not everyone may like organize for, apparently enough people do, so that it would be presumptious to say that it is not correct.
I do not know every single usage in the English language that people use that is considered correct by at least a large segment of native speakers: in New York people say stand on line to buy a movie ticket; in the rest of the USA we say stand in line to buy a movie ticket. If I said on line is wrong just because I don't use it or like it, I would not be using a very good criterion for my statement. That is why I have to check what other native speakers are saying.