This is a great question. Initially I wanted to answer only about the Palestinian side, but when I saw that the answer wiki only covers that I decided to give it a more comptehensive shot.

What both sides ignore:

Both sides ignore that, as much as we would like to think and argue, we are not at the centre of the world. People are not obliged to care about this conflict more than any other. People are not obliged to pick a side. We are just above 0.1% of the world’s population who are taking more than their fair share of the world’s headlines. And frankly, people are getting sick of this.

Both sides ignore that it is more important to think about the future than to argue about who started it all.

Both sides ignore the fact that their own media cover only half or even less of the story.

Both sides ignore that bringing our children up in fear does nothing to help them secure their future and even less to protect their mental well being. I discovered this the hard way when I took my neice to the zoo in West Jerusalem, as an 8 year old she only knew Israelis from whatever she heard in the news, in school and at home, and she was in fear for most of the journey worrying they will attack her. I can only assume that this would be the same reaction of an Israeli 8 year old. As Donald Trump qould eloquently put it: this is bad.

Both sides ignore that there are winners from all of this. People feeding on this fear and misery to gain more power and money exist on both sides and would like to keep things the way they are. These are the true enemies of peace.

What the Palestinians ignore:

Palestinians ignore that we are on the losing side. We are oblivious to the fact that we have really lost everything and we act as if we have all the time in the world. We don’t and we must give this problem the urgency it needs.

Not all, but some Palestinians, ignore the fact that if we label our struggle as one for justice, nationalistic chauvenism cannot be part of our rehtoric.

Palestinians ignore that our version of history ignores many uncomfortable truths, ones that we need to come to terms with to be able to move on.

Palestinians ignore that terms have meaning. When you use a word like genocide it actually means something, and something specific, we can’t throw words like these around as if they were slurs describing the other side.

Palestinians ignore that we cannot cherrypick when adopting a framework for a solution. We can’t say we want two states and expect to send refugees into Israel. We can’t call for human rights inquiries and complain when they call out indiscriminate rocket attacks on civilians.

What Israelis ignore (I am an outsider so this is only an outsider view):

Israelis ignore that Palestinians are a people and that they should not be expected to just accept another nation’s guardianship. It always feels to me like we are two adults trying to make a deal but Israel keeps treating Palestine as a child which has not yet come of age.

Israelis ignore that two states means exactly that. It is just unheard of that one state can have a say in another’s sovreign decisions on natural resources, borders, housing, immigration, security….. it just doesnt work this way.

Israelis ignore that we are a 20 minutes drive away. With the exception of Eilat and the far south, there is at least one Palestinian community within a 50 KM radius of any Israeli community. This means that we have no choice but to live with each other and find a way to make it work.

Israelis ignore that we are over 4 million living in West Bank Gaza and East Jerusalem. It can’t be that even a minority of us are terrorists because if only 1% were, that is a small army capable of wrecking anywhere it hits. Terrorism is not as big of a problem as it is portrayed, which means that it solution cannot be justified in collective punishment or measures that affect the eentire population.

Israelis ignore that peace comes AFTER we agree on the details. As such they cannot bring examples of acts of war to say that we can’t reach peace, afterall it is only countries in conflict that seek peace agreements.

Israelis ignore that they cannot continue to try to find old documents or quotes to say this guy is bad. People and organisations mature and change positions, and if Abbas said something in 1974 and is going against it today, his new position is, most likely, what matters.

Israelis ignore that their version of history ignores many uncortable truths which they need to come to terms with in order to be able to move on.