We consider free will important because we like to think we make our decisions based on our own individual identity, rather than physical properties of the universe that predetermine what we will do.

Even if free will exists, our mechanism for arriving at a decision to do one thing over another thing pretty much needs to be context-dependent - i.e. we make that decision based on some line of reasoning (whether correct or not).

At the same time, everything we've experienced and consider to be part of our own individual identities, the stuff that defines our free will, is incorporated as a part of that context. So many people argue that free will and determinism are still pretty much compatible.

Nevermind all the other crap we like to pretend doesn't influence our decisions like whatever crazy hormones happen to be elevated at the time.