Mr Verdan denied the father's stance was an attempt to "marginalise" the mother's partner and insisted there had been no "clear agreement", pre-conception, that his role in the boy's life would be limited to occasional visits.
Urging Lord Justice Thorpe, Lady Justice Black and Sir John Chadwick to focus on the boy's best interests, Mr Verdan said the current level of contact between them had "frozen" their relationship, which will "wither on the vine".
He emphasised that the father has no desire to undermine the role of the mother and her partner as the boy's primary carers, but wants sufficient contact with the boy to enable a "developing relationship" with his only son.
"The father described vividly to the court the pleasure and joy that he feels in interacting with his son when they see each other and the boy's responses to him.
"The father wants to play a full part in his development. He has a strong desire to develop a father-son relationship with the boy, with time spent alone with him.
"The father was at the hospital for his son's birth and held him shortly afterwards. He visited and bathed him afterwards and visited at Christmas and was later at his christening."
The father, said Mr Verdan, had been "utterly consistent" in his desire to play a father's role and it was plain before the boy was born that "he expected staying contact, time on his own" with the baby.
But Charles Howard QC, for the mother and her partner, said they had "planned parenthood" together and, had they known prior to conception the position the father would later take, they would have opted for an anonymous sperm donor.
He added: "Conflict has raged around this little boy since his birth. These kind of arrangements seem to give rise to extraordinary tensions and a sense of betrayal".
At the pre-conception restaurant meeting it had been "clearly agreed" that the boy would be brought up in a "two-parent" family, and the mother and her partner had been left with a sense of "bitterness and betrayal" by the father's demands, he said.
And he told the judges: "It is right that that agreement was reached; the court has to show more than lipservice to it and must give it considerable weight, otherwise there's no point having such an agreement."
Mr Howard said the father had been the mother's "best friend" prior to the boy's birth and, even now, she and her partner are happy for him to visit their son at Christmas and other times.
The QC denied the mother and her partner were bent on excluding the father from having "any kind of relationship" with his son.
He added: "Notwithstanding their sexuality and that they acknowledge to that extent that they are an 'alternative family', the mother and her partner hold very traditional views of family life and would not have chosen to bring a child into anything other than an intact, two-parent, family.
"The ideal upbringing for a child is a stable home in which the parents love each other and had together chosen to bring a child into the world. This is the upbringing which the mother and her partner always wanted to create for this little boy.
"Their choice of familiy life for their chiild should be respected.
"They were always of the view that their son's best interests militated against him spending very much time away from them or from his home.
"The intention was always that the father, who was at one time their close friend, would generally see the boy in their company by sharing in activities and family events.
"The breakdown of the friendship has had the result that the boy is spending far more time away from his primary parents than they had anticipated. This is something which they have had to accept but it represents a significant departure from their initial plans for their son's upbringing.
Mr Howard added: "To this particular couple, the concept of 'three parents, two homes', repeated so often by the father, is very alien and it has never been something they would consider.
"They cannot conceive of their child being shuttled, physically but more significantly emotionally, between two homes and it is something that they believe will harm their son and cause significant emotional damage.
"It has never been my clients' case that this boy does not need a male parent. Nor was it their case that his contact with his father should be limited to 'identity contact'.
The mother and her partner had never viewed the father as a "mere sperm donor" and the QC added: "They decided to proceed with a known donor, and one who was their friend, in order to provide their child with a father with whom he could form a limited but important relationship.
"There is considerable anxiety at the prospect of further destabilising their core family if contact (with the father) is extended beyond its current level."
Recognising the importance of the case, the three Appeal Court judges have now reserved their decision until an unspecified later date.
Commentary by the Ottawa Mens Centre
Notice the illogical reasons?
"could be more destabilizing", that is it they claim that their relationship has been destabilized? That's another way for saying they are unhappy the father wants to be a father of the mother's child. They completely ignore the biological fact that a child only has one real mother and one real father.