The Youth Strike 4 Climate gives me more hope than I have felt in 30 years of campaigning. Before this week, I believed it was all over. I thought, given the indifference and hostility of those who govern us, and the passivity of most of my generation, that climate breakdown and ecological collapse were inevitable. Now, for the first time in years, I think we can turn them around.

My generation and the generations that went before have failed you. We failed to grasp the basic premise of intergenerational justice: that you cannot apply discount rates to human life. In other words, the life of someone who has not been born will be of no less value than the life of someone who already exists. We have lived as if your lives had no importance, as if any resource we encountered was ours and ours alone to use as we wished, regardless of the impact on future generations. In doing so, we created a cannibal economy: we ate your future to satisfy our greed.

It is true that the people of my generation are not equally to blame. Broadly speaking, ours is a society of altruists governed by psychopaths. We have allowed a tiny number of phenomenally rich people, and the destructive politicians they fund, to trash our life-support systems. While some carry more blame than others, our failure to challenge the oligarchs who are sacking the Earth and to overthrow their illegitimate power, is a collective failure. Together, we have bequeathed you a world that – without drastic and decisive action – may soon become uninhabitable.

Every day at home, we tell you that if you make a mess you should clear it up. We tell you that you should take responsibility for your own lives. But we have failed to apply these principles to ourselves. We walk away from the mess we have made, in the hope that you might clear it up.

Students take to the street in Brighton Photograph: Martin Godwin/The Guardian

Some of us did try. We sought to inspire our own generations to do what you are doing. But on the whole we were met with frowns and shrugs. For years, many people of my age denied there was a problem. They denied that climate breakdown was happening. They denied that extinction was happening. They denied that the world’s living systems were collapsing.

They denied all this because accepting it meant questioning everything they believed to be good. If the science was right, their car could not be right. If the science was right, their foreign holiday could not be right. Economic growth, rising consumption, the entire system they had been brought up to believe was right, had to be wrong. It was easier to pretend that the science was wrong and their lives were right than to accept that the science was right and their lives were wrong.

A few years ago, something shifted. Instead of denying the science, I heard the same people say, “OK, it’s real. But now it’s too late to do anything about it.” Between their denial and their despair, there was not one moment at which they said, “It is real, so we must act.” Their despair was another form of denial; another way of persuading themselves that they could carry on as before. If there was no point in acting, they had no need to challenge their deepest beliefs. Because of the denial, the selfishness, the short-termism of my generation, this is now the last chance we have.

The disasters I feared my grandchildren would see in their old age are happening already: insect populations collapsing, mass extinction, wildfires, droughts, heatwaves, floods. This is the world we have bequeathed to you. Yours is among the first of the unborn generations we failed to consider as our consumption rocketed.

But those of us who have long been engaged in this struggle will not abandon you. You have issued a challenge to which we must rise, and we will stand in solidarity with you. Though we are old and you are young, we will be led by you. We owe you that, at least.

By combining your determination and our experience, we can build a movement big enough to overthrow the life-denying system that has brought us to the brink of disaster – and beyond. Together we must demand a different way, a life-giving system that defends the natural world on which we all depend. A system that honours you, our children, and values equally the lives of those who are not born. Together, we will build a movement that must – and will – become irresistible.

• George Monbiot is a Guardian columnist