"They're not big enough to look you in the face and come into the office and have a talk," he said.
"It's one thing for people to say some awful things, [but] when you actually have people from within the council [doing this], it's just flipping disgusting. That is where I see a risk to the organisation."
However he did not present any examples of posts he claimed were defamatory or breached the Harmful Digital Communications Act.
Feyen claimed the pages harboured hate speech, but councillor Neville Gimblett said that a definition of that term meant speech promoting violence, and the only place he had seen comments to that effect were on the mayor's own page.
Feyen said he allowed people freedom of speech on his page, but had occasionally told them to "behave". He did not deny Gimblett's claim but said he would be happy for his own page to be part of any investigation.
Gimblett told Feyen that as someone in political public office, negative comments were something that had to be put up with, unless they crossed the line into defamation.
Deputy mayor Wayne Bishop said Feyen was the risk to the council and seemed to want everyone investigated except himself.
"It seems everyone in this district is under investigation except yourself, Mr Mayor," he said.
"You want to play by your own rules and everyone who has a different view has to play by a different set."
Bishop said Feyen had been advised by council, and at "mayor school" not to use his own social media page and to stick to the official council one, but that Feyen had ignored this advice.
He said Feyen was posturing and that the council and community had become numb to his "continued antics". He said the mayoralty had become a failed experiment.
"I seriously ask you to reconsider your position as leader of this community," Bishop said.
Councillor Victoria Kaye Simmons also questioned Feyen's leadership.
She asked why he did not attend a committee set up to manage his relationship with the council's chief executive David Clapperton but had made claims on social media that he was kept in the dark over some council activities.
Feyen confirmed he did not attend the committee, and said he would not do so if he had a chief executive who could not talk with him one-to-one.
He said a vlog he had made claiming to have been deliberately excluded from an Older Persons Network meeting had been accurate as he had not received advice about the scheduling.
However Kaye-Simmons said all elected members had seen the week's schedule in their regular weekly email.
Feyen said he had not received it and they could call him or his personal assistant a liar if they wanted.
Councillor Jo Mason defined the role of a council in meeting the needs of a community under local government legislation, but said that it did not state anywhere that they had a role in controlling the opinions of others through social media.
"Sadly, your Facebook page hosts comments criticising councillors, the CE, the press and many others," she said.
"Words like "corrupt jerks" are posted there."
Mason said the mayoral role was to provide leadership to elected members and the community and to perform civic duties, as well as to meet council's plans, policies and budgets.
"What we need to do is focus on the role we are here for, this Long Term Plan you refused to sign [and] stop being sidetracked by these unpleasant, somewhat personal agendas that detract from what we're here to do," she said.
"I tend to believe you get what you focus on, so let's focus on what we're here to do. Lead this district."
Ross Campbell said he was astounded at some of the things said around the council table and that an advertisement early in the mayor's term by nine councillors had said they would not support him from the start, which was the root of much of the problem.
Bishop said that was a mistruth, and it had related to the issue of Feyen's calls for further investigations into whether the council building was earthquake prone — another bone of contention between the mayor and council.
Campbell said the inability of some to recognise the mayor and the right that he has was going to continue.
"Really, it's there and you all know it's there," he said.
He said he would vote for the notice of motion about an online investigation, but he knew it wouldn't fix anything.
The motion was lost with just Feyen and Campbell voting for it.
It was one of four motions the mayor tabled; the others were that livestreaming of council meetings should be "uninterrupted and unedited" on Facebook, that he should have access to all draft council agendas before they are publicly released, and that the council's chief executive should accept an offer from the Ministry of Business, Innovation and Employment (MBIE) to conduct further structural assessments of the council building in Levin.
The council decided livestreams would continue but not on Facebook, Feyen could receive a draft of agendas before meetings and they would not conduct further building investigations with MBIE.
