Negotiating with terrorists empowers them. That simply encourages more terrorism. The theory is the same when you are talking about Hamas bombers or Tea Party Republicans.
The debt ceiling debate went something like this: Republicans took the American economy hostage, strapping explosives to it and threatening to blow it up. President Obama sat down with them as if they were reasonable people and negotiated a deal where Republicans agreed to disarm the bomb in exchange for almost everything they wanted except the demand that Obama publicly humiliate himself by stripping naked and singing the Whiffenpoof Song on the steps of the Lincoln Memorial.
Still, the American economy is free and safe so negotiations work. Except Republicans have already started taking new hostages and demanding further concessions or they will blow up something else.
Negotiating with terrorists is weakness. It doesn't matter if the weakness is compassion (I don't want innocents killed.) or fear (What will people think of me if the terrorists fulfill their threats.). Once terrorists have seen weakness they will exploit it again and again.