When I give political opinions in cyberspace, I usually stay away from arguments that would be regarded as "religious" such as "Israel was a nation 2000 years ago and therefore is a legitimate place for Jews to live today." I would stick with what I consider the quite justifiable arguments relying on modern Zionist history; after all, modern Israel has at least as legitimate claim on her land as any nation created in the past 500 years. (How many other nations were voted into existence by other nations of the world?)
Nevertheless, the argument from ancient Israel has merit as well, even to a secular audience. You do not find Italians praying for the re-establishment of ancient Rome or anyone longing for Assyria, Canaan, Babylonia or any other ancient kingdom.
But Jews have NEVER reliquished their claim to Israel. Daily prayers ask for the rebuilding of Jerusalem. Jews have almost continuously been trying to move to Israel, an area with almost no natural resources, since the Roman conquest. Jewish immigration to the area pre-dates modern Zionism by many centuries (look at the history of Safed/Tzfat, for example.)
Further evidence comes from what happened since the establishment of the state. A significant percentage of world Jewry now lives in Israel, even though they can easily choose to move to other places. The only reason for this is because for Jews, Israel does have an emotional pull that no other place has.
The Jewish claim to Israel is not modern; it truly is ancient and continuous. And this claim is nothing to be embarrassed about. An emotional tie to the land is just as strong, if not much stronger, than a political or nationalistic claim.
Right now the second and third holiest Jewish sites in the world (the Cave of the Patriarchs in Hebron and Rachel's Tomb in Bethlehem) are in trouble. The only argument for keeping them in Jewish hands is purely emotional. But that is a strong argument! Not everything is logical, and the love that the Jewish people have for Israel is not logical as well. But it is there, and it is what will ultimately win the battle for Israel.
Don't think that the Palestinians don't use their fictional emotional argument to score points as well. They made up an entire history of their people (as well as delegitimizing the Jewish historical ties to the land) with that exact reason in mind. On demand they can produce throngs of wailing women; perfect for the 6:00 News. How can a lawyer argue with crying women?
The reluctance to use the emotional argument hurts Israel's PR efforts. When Israel makes its arguments rationally of her rights, that implies that a better counter-argument would destroy Israel's right to exist. But emotional arguments cannot be argued against.
We all know about the double standard that Israel is subjected to, that Israel is expected to act in ways that no other nation is expected to. A major unspoken assumption in the double-standard is that Jews are rational and therefore can be expected to act rationally. Of course there has to be some sort of territorial compromise, this thinking goes; so the Jews should understand that and do the right thing. But the Arabs cannot be reasoned with - they are emotional, they might engage in terror, they might incite the "Arab street", they might raise the prices of oil if we anger them - so keep them happy. Israel won't act irrationally, Israel wouldn't hurt the someone because of a perceived insult, so only Israel can be expected to make concessions.
There is great tactical advantage in sometimes going crazy. I have a friend who would, about once a year at work, just start shouting at some departmental meeting for no good reason. He did this to make the boss tiptoe around him a little, to treat him a little more deferentially, because who knows what will make him go off? It was a rational decision to be irrational.
When Israel uses the emotional argument, no one can tell her to think clearly. The Tomb of the Patriarchs will never be in non-Jewish hands again, ever - this is a red-line statement that should be made. Jews have the absolute right to live anywhere they want in the Middle East, especially in Biblical Israel - another non-negotiable statement, not open to compromise or reason. We can argue it is important for security until we are blue, but security can be mitigated in theory - people's feelings cannot be. Transferring Jews out of their ancient homeland is more of a crime than transferring Arabs out - why is saying such a statement forbidden in diplomatic circles today? Only because we try so hard to be rational, to be intellectual, to use our brains and not our hearts.
Even without resorting to biblical arguments, the emotional argument is not being used. Imagine the pain of having to move out of your home where you lived for decades, where your schools are, where your cemeteries are - how come these arguments are so muted? Isn't that argument at least as compelling as any that is for the transfer of Jews?
But the winner in a battlefield in the end is usually the one with the most heart. If Palestinian Arabs are being taught from birth that their homeland is in that narrow strip of land, every Israeli kid should be taught the same - with the added benefit of its being true! And this is why you cannot discount the chances for the tiny number of Gaza Jewish residents to win: they have more heart.