Your argument seems to hinge on the assumption that all the islanders know that there are only two eye colors present on the island (along with more subtle errors).
The original puzzle says that there are an unknown number of eye colors (which happens to be just blue or brown, but the islanders don't know it), and the only reason blue-eyed people are killing themselves is because of the foreigner's statement; note that none of the brown-eyed people kill themselves in the inductive solution, because one of them could be (e.g.) green-eyed but not know whether or not they are the only one. The fate of the brown- and blue-eyed people would be reversed if the foreigner said "I see a brown-eyed person" instead.
As for the more subtle errors, let's assume there are only blue or brown eyes and the islanders know this. Now suppose A is brown and B and C are blue. Then B and C each see one blue and one brown. I think you'd agree that without a foreigner coming to the island and telling them that blue exists, neither can tell which their own color is. But A sees two blue -- exactly the same as in your example of three blue. So if A is using your reasoning: Day 0: no one dies. Day 1: no one dies. Day 2: no one dies. Day 3: B and C still have no idea what their color is, but A, seeing the same eyes as the A in your example and no one dead yet, commits suicide believing he has blue eyes, even though he does not. Clearly A's logic is faulty.
The original puzzle says that there are an unknown number of eye colors (which happens to be just blue or brown, but the islanders don't know it), and the only reason blue-eyed people are killing themselves is because of the foreigner's statement; note that none of the brown-eyed people kill themselves in the inductive solution, because one of them could be (e.g.) green-eyed but not know whether or not they are the only one. The fate of the brown- and blue-eyed people would be reversed if the foreigner said "I see a brown-eyed person" instead.
As for the more subtle errors, let's assume there are only blue or brown eyes and the islanders know this. Now suppose A is brown and B and C are blue. Then B and C each see one blue and one brown. I think you'd agree that without a foreigner coming to the island and telling them that blue exists, neither can tell which their own color is. But A sees two blue -- exactly the same as in your example of three blue. So if A is using your reasoning: Day 0: no one dies. Day 1: no one dies. Day 2: no one dies. Day 3: B and C still have no idea what their color is, but A, seeing the same eyes as the A in your example and no one dead yet, commits suicide believing he has blue eyes, even though he does not. Clearly A's logic is faulty.