Calling him such as you have is unfair to douchebags, which actually have uses.

Personally, I think douchebag is the most feminist of insults. There are so few medical or otherwise practical purposes for douching, it's mostly deployed as a device for making women hate themselves. It really is a gross symbol of oppression, and to call someone a douche or a douchebag is, to my mind, a radical action. Particularly given the prevalence of oppressive shaming words like "big blubbering vagina" or "pussy" or "boob" or "tit" or even "dick" or "cock". And that's without even going near words like slut and cocksucker, which are a whole extra level of problematic.