それでも is a combination of the 代名詞(だいめいし) (substitute noun)
それ, and the 副助詞(ふくじょし) (adverbial particle)
でも. It is often translated simply as ‘even so’, or ‘nevertheless’. Literally, it is a bit closer to ‘even with that’.
それでも is usually used between an (A) and a (B) phrase, to show that there is more information (usually surprising) to be considered.
-
今日(きょう)は雨(あめ)が降(ふ)るよ、それでも釣(つ)りに行(い)くの?
It's going to rain today, even with that, are you still going fishing?
-
私(わたし)は殴(なぐ)られたり、蹴(け)られたりするのが嫌(きら)いです。それでも、空手(からて)が好(す)きなので辞(や)めれないです。
I don't like getting punched or kicked, even so, I like karate so it is hard to quit.
This grammar point primarily expresses that ‘even with’ what has been said previously, it is not all there is to think about.