After his wife, Pauline, left him in May last year, the CSA decided that he should pay pounds 574 a month maintenance to support their children, aged 9, 11 and 13, and pay a carer's allowance for their mother.
Expenses such the cost of having his children to stay at weekends and taking them on holiday - and the pounds 400 a month cost of travelling to work in London from his home in Braintree, Essex - were not taken into account when the CSA decided how much he could afford to pay. Nor does the agency consider the cost of debts incurred while married for the benefit of the family.
Even though Mr Gibbons, 43, had paid all the mortgage on the marital home and even though he never wanted her to leave, he agreed to give her half the value of the equity to help set up a new home.
He had wanted to increase the mortgage to release capital to pay her a lump sum, but the CSA would not allow the costs of an increased mortgage. It would only allow 'reasonable' housing costs.
And so, because he wishes to give his ex-wife money to provide a house so the children will not suffer, he has put their home on the market and plans to rent a small flat instead.
Another grievance is that although he wrote several letters to the CSA explaining that he could afford to pay only pounds 400 a month - which he paid - the agency never replied and instead issued a 'deduction from earnings order' forcing his employer to deduct the maintenance from his salary. That was the last straw.
Mr Gibbons decided he was not prepared to spend 13 hours a day travelling and working in London to be left with about pounds 300 a month to live on and keep his children at weekends. So last month he resigned and he plans to set himself up in business as an accountant, working locally.
'My only hope is that the Government sees sense and changes the rules,' Mr Gibbons said. 'The CSA takes no account of people's individual circumstances. Everyone is supposed to fit into a rigid formula. The whole process is dehumanising.
'The upshot of all this is that I have been forced to put my house on the market to pay my wife off, for leaving me. This in turn will mean that it is unlikely that in future I will be able to have my children at weekends, as any future accommodation will inevitably have to be smaller. Since the formula ignores essential costs such as travelling to work, I have tendered my resignation. As my income will be small while I'm self- employed, not only will the state have to support my wife and children, it will also have to support me.
'I cannot believe that the CSA was established to create a situation whereby a father who has been doing what he can to support his children, and also make bearable what is a traumatic experience for everybody, is forced by the inhuman approach of a government agency to relinquish everything he has tried to build up for his family over the years.'