The leader of the council’s Labour group has said he is angry at the change of heart and is calling for a special meeting of the council to discuss the decision.
Falkirk Council’s Children’s Services says all parents have been given the option not to allow their child to participate in the Scottish Government’s health and well-being census.
The survey, which has different questions for different age groups, was sent to pupils to get views on a range of issues, including the pressures of school work and bullying.
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However, the section for pupils in S4 to S6 caused an outcry with explicit questions about pupils’ sexual experiences and contraception.
One question asks about pupils’ sexual experience, with multiple choice answers including “oral sex” and “vaginal or anal sex”.
Others ask about contraception methods and what age they were when they had sex for the first time.
Pupils from S2 upwards are also asked to reveal if they have used alcohol, tobacco or drugs.
When concerns were first raised, Falkirk was one of ten councils that withdrew the survey.
But the local authority now says it has “reviewed the contents and various opt-outs” and decided to proceed.
A spokesperson for Falkirk Council said: “We originally delayed our position to examine closely any concerns that were raised about the survey prior to Christmas.
“Following a review of the contents of the survey and the various opt-outs available to both parents/carers and young people themselves, we decided to progress with the survey.
“Parents/carers received a letter indicating the purpose of the survey and were given the option not to participate.
“We have discussed the survey with the political group leaders within the Council.”
However, the leader of the council’s Labour group says councillors were not consulted – or even shown the survey.
Councillor Robert Bissett said: “I was told by the Director of Children’s Services that the survey had been dropped.
“In late January he called me to say it was going ahead – but there was no agreement from me.
“My view was still the same and I made that clear.”
Mr Bissett said that he is now trying to get a special council meeting to discuss it.
He added: “I learned of the survey from a friend in West Lothian and I got the survey from another authority who rejected it, so it was not shared with councillors.”
The Scottish Government says that surveys like this “play a crucial role in ensuring children and young people have access to the help, advice and services they need”.
They argue that the long-running surveys have included questions on topics including sexual health and well-being, substance use, alcohol consumption and smoking.
Speaking in the Scottish Parliament, First Minister Nicola Sturgeon told MSP’s: “Either we can bury our heads in the sand and pretend that young people are not exposed to the issues or the pressures that we know they are exposed to – or we can seek to properly understand the reality young people face and then provide them with the guidance, the advice and the services they need to make safe, healthy and positive decisions.”