In the end, it boils down to an unspoken “All for one and one for all” Israeli aethos – the same reason that people will follow the story of any Israeli who gets lost in some jungle in the farthest corner of the world, and people here will donate their time and money to go looking for him/her. I can’t really explain, it’s something in the Cultural Genome 
And of course, the misgivings and downsides don’t really need explaining – it motivates Hamas and other groups to try and kidnap more Israelis; it strengthens Hamas and by proxy other violence-backing groups against the relatively moderate Fatah; it motivates individuals to commit acts of terrorism knowing or at least hoping that they will be released in the next deal… And last but not least it is a breach of a promise we make to the families of previous victims that we will catch and punish the perpetrators.
And still, the blood of one living person really is redder than that of all those who have died. And while the silly grin on the faces of everyone yesterday, from the man on street up to the most hard-boiled newscasters, may in fact be a sign of a nation gone mad, it’s still a Beautiful Madness IMO.
Or, to put it differently, there comes a time when you just have to do something in order to be able to live with yourself. Even if you know you’ll pay the price later. And when all is said and done, yesterday I was proud of my country, and proud to be an Israeli.