Many have become disillusioned with the idea of a negotiated two-state solution for Israelis and Palestinians. They think that a deal is unachievable and the two peoples are incapable of the necessary compromises. They are calling for an abandonment of the two-state paradigm, or for the international community to impose a solution at the UN. Some even think the conflict can be resolved by boycotting Israel in order to bully it into accepting all of the demands of the Palestinians.

But those who have lost faith in a negotiated two-state solution are underestimating the capacity of Palestinians and Israelis to look beyond their current disagreements and conceive of a better shared future.

A recent event facilitated by Bicom illustrated this. We organised an unusual roundtable discussion in Israel for a group of young media professionals from the UK. The guest speakers were a young leader of the centre-right Israeli Likud party from Tel Aviv and a young Palestinian activist from the Fatah party in Ramallah.

The two had an unusual story to tell. They had met in the context of an internationally sponsored forum for young Israeli and Palestinian leaders. Despite their deeply entrenched and firmly opposed personal and national narratives, they had struck up a close friendship, clearly visible in the warmth they showed for one another.

Over the course of the discussion each of them spoke about the conflict from their perspective. Their versions of the present reality and how we got here were starkly different. But they did not argue with one another. They listened respectfully to each other's stories.

The Likud activist spoke for both of them when he told the British participants, "I don't expect the other side to accept my version of events, but it is important that we each learn to understand how the other side sees the situation. On this basis we can build a shared future."

This is the key to resolving the conflict. Both sides have core strategic concerns that need to be reconciled. Neither side is going to abandon its national narrative or its claim to self-determination. What these two had learned through meeting one another was that the conflict cannot be resolved by one side forcing the other to accept its claims.

The only way to solve the conflict is if each side comes to understand the other side's claims, and finds ways to reconcile competing demands through dialogue and negotiation. This will require considerable flexibility and difficult concessions on both sides. But these concessions can be made if leaders on both sides can convince their publics that the deal represents the best available option.

A former Israeli negotiator told me: "You need to think about the other side's victory speech." In other words, peace cannot be a zero-sum game. In order to reach a final status accord, each side needs to think about how the other side will sell the deal to its constituents. The leaders on both sides need to be able to set out a vision for a post-agreement future, which will be better for their children than the status quo.

From my long experience of Israel, I have learned that most Israelis would be ready to back the establishment of a Palestinian state in Gaza and the West Bank. This is consistently confirmed by opinion polls. However, they can only be sold on the deal if their core requirements are met in return. In essence, in return for Israel giving up its control of the occupied territories, the Palestinians have to give up their claim to the territory which is now Israel. This means there cannot be a mass return of Palestinian refugees to Israel.

This is why the Palestinian attempt to have their claims endorsed at the UN is not only misdirected, but also dangerous. For negotiations to have the best chance of success, both sides need to go in with as few constraints as possible.

Each side will bring demands, but they must be prepared to moderate them. If the UN endorses maximalist Palestinian positions, it will make it harder for them to compromise on them around the negotiating table. As well as complicating future negotiations, the Palestinian leadership is creating expectations among its public that will not be matched by real change on the ground.

Two states remain the only conceivable solution that balances the needs of Israelis and Palestinians. The international community must promote an environment which makes that negotiated two-state solution more likely. They must avoid steps at the UN which will make it harder for either side to make painful but necessary compromises in the future.