Catholic education is seen as a threat by some members of the DUP, their partners in government have claimed.
The DUP wants to create a vision of schoolchildren who are all Northern Irish, Sinn Fein MLA John O'Dowd added.
DUP leader Peter Robinson has hinted that, while church schools are welcome to exist, the state may not be obliged to fund them. He compared the Northern Ireland education system to South Africa during apartheid when black and white children were taught separately.
But Mr O'Dowd argued: "They see the Catholic education system as a threat to their vision of society, not even in terms of Catholic religious teaching or theology but in terms of how the nationalist community is educated.
"The DUP wants to break that down and turn society into a schooling system where at the end of it we produce a ceramic vision of each other where we are all little Northern Ireland, and I think that is a mistake in itself."
He told the Assembly nobody could argue against integrated education but added parents had a right to choose where to send children and in most cases they went to their local school.
"We live in a divided society, so naturally many people in the Catholic community send their children to Catholic primary schools or Catholic secondary schools, and within the unionist community they are sent to controlled schools," he said.
"That is as a result of our society - it is not education's fault that we have a divided society."
He said co-education was part of the solution but was not the only answer.
DUP MLA Michelle McIlveen supported her leader's comments.
"Since we don't educate our children in separate universities, why do we teach them in different schools? By doing so we become entrenched in our differences," she said.
The debate was prompted by Alliance Party MLA Trevor Lunn.
"The statistics of empty desks, school building and maintenance programmes in disarray, and a crumbling school estate point the way towards a massive and urgent need for cross-sectoral co-operation as an absolute imperative," he said.
"Does anyone still doubt the economic, educational and social benefits of more sharing and integration? If so, they are living in a different world to me."
The Alliance Party motion was passed.