This is a question I'm having a difficult time understanding for my Philosophy course. I know it has to do with Derrida and Levinas and I know it has to do with the ideas of the Same and the Other. Other than that, I'm quite lost. Can someone possibly explain this concisely to me? I have written a first draft but want to make sure I'm on the right track.
It to be responsible to the Other (often for the Other) is a term central to Levinas's philosophy. Depending on where exactly you read this in Levinas, he will articulate the same point in different ways. But the basic idea of responsibility is captured in the natural understanding of the word "responsibility" but then amped up to infinity. The basic idea is that you place the other before yourself and consider their existence more important than your own.
The key to answering the question you're working on here is understanding how the words "self" and "Other" are used in Levinas's philosophy (or in Derrida's critique). One problem is that the word self has many meanings. You probably won't be too far off if you think of as moral self that has consciousness. The "Other" is also a type of morally relevant being but one that for the self is not the self (Levinas doesn't write much about whether it is a self-for-Others itself). Levinas calls the sort of moral behavior that seeks out the Other desire or the sort of willingness to sacrifice everything responsibility.
When we are talking about diminishment of self, we are referring to a different definition of self. Here, we mean the self championed by Descartes and others that is autonomous rational and understands its world. Levinas's point is that you cannot be the "captain and commander" of your world while simultaneously surrendering your rights, thoughts, and framing abilities to serve the Other.
Derrida's critique is that to recognize something in my world as an Other requires me to engage in precisely the sort of categorizing that supposedly is the problem.
Other than this kind of basic sketch, I would need to better know what you are having trouble with to answer with relevant passages or details. (I wrote my dissertation on moral selfhood including a chapter on Levinas).