As other people have said, they've seen worse Everton sides go right to the final day and stay up, none of them were admitting defeat with 18 games to go.
This season there's 3 points between the bottom and 14th. As it stands all of those teams are in the mire - I gaurentee if we were sitting where Leicester are in 14th there'd still be people on here adamant that we're going down just like last season even though we'd all give anything for that now.
I believe a decent manager can get us 6 or 7 wins and a handful of draws from our remaining fixtures which should be enough to stay up and add a few half decent signings to that and it looks even better.
But i'm a realist also, were not in a good position, worse than last season so yes of course we can go down, very good chance of it but there's still a chance we can turn this around and stay up. Let's just wait and see. Some of us are so defeatist and that negativity spreads and seeps in. We need to be behind the team and new manager and have belief they can turn it around - not giving up and admitting defeat when there's 18 games and 54 points to play for! We're not down til we're down so until then let's just have a bit of belief. It's football anything can happen.