Trollip was addressing the media after a council meeting on Tuesday after Democratic Alliance (DA) leader Mmusi Maimane had earlier condemned Bobani's behaviour.
"There were some people who had a blind spot with regards to councillor Bobani and in fact the United Democratic Front leadership Bantu Holomisa in particular has a blind spot with regards to this councillor," said Trollip.
Last week Trollip took a decision to axe Bobani from his mayoral committee team heading up the public health directorate. Trollip said the pubic health directorate had been a concern for a number of months, citing allegations of maladministration which were being investigated internally.
The decision followed months of simmering tensions between the two who have been at loggerheads over a staff appointments and issues around governance.
Subsequent to Trollip's decision, Holomisa came out guns blazing in support of Bobani and basically accused Trollip of making a decision without consensus.
On Monday, coalition partners and party leaders Holomisa and Mmusi Maimane of the DA met and issued a statement saying the coalition government was "stable" and the ultimatum put to the UDM to remove Bobani as the deputy mayor had been withdrawn.
However, the next day, the DA changed its tune in that Maimane issued a statement saying that he condemned Bobani's actions during Tuesday's council meeting.
During the council meeting Bobani took aim at Speaker Jonathan Lawack, who had asked him and another ANC councillor Siseko Plaatjies to leave chambers because they were becoming disruptive.
"I'm not going anywhere, I'm the deputy mayor, unless you want to collapse this meeting... you are abusing your powers," retorted Bobani.
Both Bobani and Plaatjies refused to leave council chambers. Trollip told reporters that Bobani's actions at council served to reinforce every complaint that he had made to their national leadership.
"His conduct does not speak of a coalition partner, it speaks of having an enemy behind our own lines. It's like being in a circular firing squad it is an untenable situation. My decision to remove councillor Bobani from the mayoral committee position for public health is because there has been a break down of trust, a break down of cooperation and in fact even a break down of proper administration and service delivery in that department," said Trollip.
Trollip made reference to Bobani's behaviour at council as well as the protest which took place outside the building by UDM and Cope members who denounced Trollip and called for Bobani to lead the Bay.
"It is all an expose of what has been transpiring here for the last five months that I have been trying to deal with at a national level. It has become untenable, the relationship has broken down to such an extent that I cannot continue with councillor Bobani as one of my mayoral committee members," said Trollip.
Meanwhile, earlier on Tuesday during a brief council adjournment, ANC, EFF, African Independent Conference (AIC) and UF councillors started cheering on in support of Bobani. "We don't want Trollip, we want Bobani! Mayor! Mayor! [Bobani]" ANC councillor's were heard chanting.
Responding to a question on speculation that Bobani might be garnering support from the ANC in a bid to oust Trollip, the mayor responded: "I can't speculate what councillor Bobani does behind close doors or [within] enemy ranks, it's very difficult to tell you what he does in our ranks as a coalition partner," he said.