Literal translation
it affects him as much as the plague affects cats
Meaning
it leaves him completely unmoved
Explanation
This comparison signals a total indifference toward a threat or remark that would worry most people. The literal image draws on an old popular belief that cats were spared by the plague, unlike the rats that spread it and the humans who died of it: the cat goes about its business untouched by the scourge. To say that something affects someone the way the plague affects cats is therefore to say that it does not touch him at all, that it slides off him without a trace. The turn of phrase has a rural, old-fashioned flavour, inherited from a time when epidemics shaped village life and supplied a stock of strong images for indifference or, conversely, disaster. The register is familiar, used with a touch of admiration or exasperation depending on context, to underline how unshakeable someone remains in the face of news that should, by all logic, rattle him.