Mr Bennett, who was recovering from a stroke, was allowed to board the flight early.
Having taken the sleeping pill prescribed by his doctor, he promptly fell asleep and could not be woken. A flight stewardess declared him a "medical emergency".
In spite of this, Mr Bennet was eventually able to awake from his sleep and tried to explain he had taken medication before the flight.
Talking to the BBC he said there might have been some confusion, as his wife's first language is not English.
"It was so humiliating," he said. "Basically, the stewardess became judge, jury and executioner."
In a statement to Fox News, WestJet insisted that the decision to remove him was the correct one.
The airline's spokesperson said he was being removed for being "under the influence of drugs", not for sleeping.
According to the federal transport guidelines if a passenger shows signs of not being 'fit to fly', they will be removed from the flight.
WestJet's stance is to include "significant impairment arising from the consumption or use of alcohol or drugs prior to boarding."
"We stand by our crew's decisions and believe that what we have offered to this guest is reasonable under the circumstances" the airline said in a statement.
The Bennett family, who were travelling to Cuba as part of a package holiday, were told by Westjet they could fly on the next service scheduled for the following week – missing out on much of their vacation.
Instead they decided to buy seats with another airline, which cost the Bennetts C$2,000 (NZ$ 2,290) in fees for flights and a night in Toronto hotel.
The family said they are seeking compensation and an explanation for his rude ejection from the flight, in spite of travelling with a doctor's note outlining his fitness to fly.
