Aguero, 33, joined Barcelona as a free agent this week after his contract with City was not renewed.
Aguero, City's all-time top scorer, played his last game for the club in the Champions League final defeat to Chelsea on May 29.
When asked about Guardiola's emotions, Aguero's father told Argentinian station Radio La Red: "I don't believe him. No, I don't. I believe he never wanted him [Aguero]."
Asked if the tears were for the cameras, he added: "Of course. He wants to be the star of all the teams he is in instead of the players.
"It's incredible. He [Guardiola] says he is irreplaceable, and he doesn't have him in the squad. These are things of Guardiola, he is a great coach. But from one day to the next he changes the players and you never know if you are going to start or not."
Del Castillo also said his son's wish was to renew his contract with City but the offer never arrived.
"There's someone that tells you that you are no longer able to continue at the club and you have no choice but to change [clubs]," he added.
"He waited until the last minute to see if he would renew with City but it was not possible. They didn't want to."
Aguero's father revealed his son had options to continue playing in England but opted to join Barca instead.
He signed a two-year contract with the Catalan giants, a move that will see him play with compatriot and friend Lionel Messi, should the latter sign a new deal with Barca this summer.
"They [Messi and Aguero] have been friends since they were 15. They have always talked. I'm certain they will play together."
The former Atletico Madrid forward tested positive in a rapid test for COVID-19, only for his PCR to come back negative.
Aguero tested positive for COVID-19 in January and has not been vaccinated, according to his father.