I wouldn't go so far as to make an absolute statement that self-defense is a sin, although I would suggest that orthodox teaching, and examples like that of the desert fathers suggest a different approach to conflict as an ideal. But I don't think that approach is easily simplified to absolute and universally applicable moral propositions. But let me cite a story from those desert fathers:
"There was a great hesychast in the mountain of Athlibeos. Some thieves fell upon him and the old man began to cry out. When they heard this the neighbors seized the robbers and took them to the magistrate who threw them into prison. The brothers were very sorry about this and they said, 'It is through us that they have been put in prison.' They got up and went to Abba Poemen to tell him about it. He wrote the old man saying, 'Consider the first betrayal and where it comes from and then examine the second. In truth, if you had not first failed within, you would not have committed the second betrayal.' On hearing Abba Poemen's letter read (for he was renowned in all the district for not coming out of his cell), he arose, went to the city, got the robbers out of prison and liberated them in public."
From this and other stories it's clear that as an ascetic ideal, not doing harm to anyone else, being self-sacrificing, was considered a highest principle. The "failure within" is a failure of dispassion, that is, the ideal of a truly dispassionate life in which one would not even cry out at the sight of robbers, because one has "perfect" love as God, who "makes it to rain upon the just as well as the unjust." But should this picture of an ideal love be absolutized or rationalized to mean that a young woman couldn't defend herself against a rapist? Or a parent act in self-defense? Not everyone is a monk. The ideal exists as a symbolic reminder of Christ's love, as a principle it reminds us to be aware of our normal tendency towards narrow self-interest. But it shouldn't be an absolute such that any self-defense is inherently sinful. Discernment and economy are also important notions in orthodox morality.