I come to it after the test question:
In this case you need "lo que" because it is referring to "The thing that", as a neutral thing/idea. So, we could say:
"The thing I hate about you is your coldness." or "What I hate about you is your coldness."
There is a very similar example in the lesson:
Lo que admiro de ellos es su tenacidad.What I admire about them is their tenacity.The thing that I admire about them is their tenacity.
I hope this helps.
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