For the Everton defense, problems aren't so huge.
With Leighton Baines, Phil Jagielka, Sylvain Distin and Tony Hibbert, the back four is in very good shape. Most of the dilemmas are concerning the attack, which last year, wasn't as good as it could have been.
However, the backbone of the defense is Phil Jagielka. As an extremely strong player, he is an intimidating presence and isn't exactly the ideal player that you want marking you.
In recent years, Jagielka has been an absolute beast, and therefore he is a target for several teams, namely Arsenal. The Gunners evidently need a center back, because even though they already have Thomas Vermaelen, the contenders for the other half back are quite shaky.
Arsene Wenger has shown that he is greatly interested in the Englishman Jagielka, as he already made a ₤10 million bid for him. However, this attempt to snatch "Jags" proved quite insulting for the Toffees, as they had just rejected a ₤12 million bid last summer! Everton fans found it offensive that Wenger would go below a bid that had already been declined.
If a report from the Daily Mail is correct, then only a ₤20 million Arsenal bid would work. For Arsenal, it is probably right to pay that much money for Jagielka, given the current state of their defense.
But from the Everton standpoint, is it worth giving him, even for the large amount that they demand?
Sure, if Jagielka leaves, they could always sign a big, strong defender just like him; Christopher Samba, Scott Dann or others.
Let's say that Jagielka has gone to Arsenal. Will another center back be able to fill the shoes of Jagielka, with all the knowledge of the team, the leadership, the chemistry with other players, etc?
And it sure won't be easy, especially the new signing's first year to blend in with Everton, and effectively replace the English center back.
For Everton, if their is even a small chance of risking their defense as it currently is, they probably shouldn't do it. And the chances are, if they do try to replace Jags, he won't play the same role and be as good for the Toffees.
This probably isn't a thing money can fix, either. Even if Everton demanded ₤30 million and it was accepted, the replacement still wouldn't be able to do everything the same way as Phil Jagielka.
Therefore, in conclusion, I don't think Everton should do this deal with Arsenal if it means losing their precious center back Phil Jagielka.