The way I reconstruct your argument does not imply that all science is bad. The argument presupposes a distinction between science and scientism. Your idea, as I understand it, is that because science works by analyzing concepts we already know before we ever do any science, not all knowledge is scientific or a part of science, i.e., scientism is false.

I read you as giving a reductio ad absurdum argument against scienticism, i.e., the view that science is the only source of knowledge. Here's how I reconstruct it:

1. Suppose scientism is true (i.e., suppose the only source of knowledge is science).
2. Science only analyzes pre-existing concepts. (assume)
3. Pre-existing concepts that science analyzes are known prior to science. (assume)
4. Therefore, the source of some knowledge (viz., knowledge of pre-existing concepts) is not science. (from 2, 3)
5. Therefore, scientism is false. (from 1, 4)

Would you say that's a faithful reconstruction?