Mr McKeague, of Dunfermline, Fife, was 23 when he vanished in the early hours of September 24 2016 after a night out in Bury St Edmunds.
Suffolk Police believe the airman, who was stationed at RAF Honington, climbed into a bin which was then tipped into a waste lorry.
Mr McKeague’s father Martin McKeague said in a statement read by lawyer Peter Taheri, counsel to the inquest: “Corrie was a happy child, however there were major events that shaped Corrie’s life.
“When Corrie was 10 years old Nicola (Urquhart, Corrie McKeague’s mother) and I had separated.
“At the age of 15, when he was first to find the body of his friend who had just been killed on a train line, I believe Corrie developed a significant binge-drinking problem.
“In his teenage years that impacted his emotional wellbeing and looked at many of his relationships.”
He said that his last contact with his son was on his birthday, September 16, “when I sent him a message to wish him a happy birthday and I sent him money”.
He said the death of his son’s friend “was a terrible shock for a 15-year-old boy to suffer, and one I don’t think he ever truly got over”.
Mr McKeague continued: “I don’t believe Corrie was ever suicidal.”
Corrie McKeague: Former airman died after climbing into industrial waste bin whi…
Mr McKeague’s mother Nicola Urquhart, in a statement read to the inquest in Ipswich by lawyer Adam Walker, said one of her son’s “very close female friends was hit by a train and killed instantly”.
“This event had a huge impact on Corrie,” she said.
She said Mr McKeague had started to train as a hairdresser, then as a PE teacher, before joining the RAF.
While he was prescribed antidepressants in the past, she said he was “back to his usual happy self” by 2015.
Ms Urquhart said her son “regularly lost his phone or wallet on nights out” but “was never aggressive with or without alcohol”.
“There was nothing to suggest Corrie had any problems or concerns around the time of his disappearance,” she said.
She said he had told her that he had “bumped a taxi on one occasion, meaning he had run off without paying”.
Suffolk’s senior coroner Nigel Parsley said Mr McKeague, who had served in the RAF for three years, drank a “significant amount of alcohol during the evening” of September 23.
He said Mr McKeague was asked to leave Flex nightclub and “was seen on a number of occasions on CCTV”.
“He’s seen to sometimes be alone, sometimes in conversation with others and seen to obtain food,” Mr Parsley said.
He said that at 3.25am on September 24 CCTV captured Mr McKeague entering a horseshoe-shaped area in Brentgovel Street.
“You might find based on evidence that 3.25am is the last time Corrie was seen and known to be alive,”
He said jurors will hear evidence about Mr McKeague’s movements on September 23 and 24, his contact with any witnesses and “hypotheses and possible scenarios relating to Corrie’s disappearance”.
The inquest, due to last for up to four weeks, continues.