Here's a breakdown of its etymology:
* Latin: *evadere* (to escape, to avoid)
* Late Latin: *evasus* (escaped, avoided)
* Old French: *evaisir* (to escape, to avoid)
* Middle English: *evade* (to escape, to avoid)
* Modern English: *evasive* (tending to avoid giving direct answers, tending to escape or avoid)
So, the word "evasive" literally means "tending to escape or avoid", which is why it's used to describe someone who is trying to avoid answering a question directly, or someone who is trying to dodge responsibility.