Quite a negative definition of being oneself! I think as long as you are putting the emphasis on others, even though in order to try not to be like them, you are not genuinely being yourself. I think one should not go out of one's way to try not to sound like others, but rather try to positively write what one is genuinely inspired to, what one's inner psyche dictates. In this sense, listening to others' music as a source for compositional ideas (let alone trying to consciously follow their lead or avoid doing so) can possibly even act as a deterrent to originality or being oneself. As a concrete personal example of this, I used to listen to music a lot more before I became more active as a composer.
My own definition of "being yourself" would be the following (as already hinted at in the paragraph above): listening to one's own inner voice and trying to compose what it dictates, in the final analysis regardless of one's potential audience's perceived or anticipated reactions, and without any attempt to please or earn their praise. I believe that genius and originality are never (and ought never be) about seeking one's audience's approval or praise, or the reward that would accompany such approval and/or praise. While approval and praise could serve as objective indications or objective criteria of one's success as a composer, they are only the indirect outcome of true originality and the true discovery of one's voice as a composer, never the aim themselves. Should they become the aim (or the conscious aim at least), the music becomes reduced into a mere means to garner praise and social approval and, in my opinion, falls short of the requirements for being characterized as original!
"Being oneself" would also mean to compose music related to one's experience and being, and somehow expressing them; not trying to imitate others (whose original music would have come from their own unique experience which one does not and cannot share).
I think being original is a challenge in the sense that one has to be oneself in a context of others. Hence one has also to relate to others; to take others' (and humanity's in general) being, experience, and behaviour into consideration (in going about being oneself); to find an ideal balance between these two (being oneself and taking others into consideration) such that one's being oneself (precisely as a composer, insofar as one is composing for any audience, even oneself - in the sense that one exists in a social context and hence becomes oneself FROM it or proceeding from it) is meaningful to others also, communicates something of relevance to others also, and yet such that one's attempts to be meaningful to others and to address others do not get in the way of one's self-fulfilment, self-realization and self-expression as a composer. After all, one has to fulfill oneself and be oneself among other people, unless one plans to live in solitude (but even solitude proceeds from and is a getting away from - and hence takes for granted being in - a society). But composition, to me at least, is a social act. It is the distillation of social experience through the unconscious and the psyche. Even personhood is to some extent socially created. To me composition is not only an act, but a process of active becoming. Perhaps composition is one form of self-creation.
Finally, I think being original is often more about saying the same things (others have said before one) in new ways, than about saying something new in the same way (others have said before one).