William Payne, 54, was also accused at a Fatal Accident Inquiry of lying by not telling the DVLA he had a history of blackouts, which could have stopped him being on the road.
Mr Payne faced the claims as he was questioned in public for the first time about the deaths of Mhairi Convy, 18, of Lennoxtown, East Dunbartonshire and Laura Stewart, 20, of Cumbernauld, North Lanarkshire.
The accounts students at the former Central College of Commerce were struck by Payne's car after it ran up on a pavement in North Hanover Street, Glasgow, in 2010.
Criminal proceedings against him in connection with the incident were dropped last year by prosecutors. The FAI was then arranged to look at the circumstances of the deaths.
Mr Payne faced a series of questions yesterday at Glasgow Sheriff Court from Dorothy Bain - the QC representing the families of the two women - but he refused to answer many of them.
Sheriff Andrew Normand had earlier told him he did not have to answer any that may show him to be guilty of a crime or offence.
Miss Bain questioned him on the renewal of an HGV licence in July 2010 - five months before the accident.
The QC said the No box was ticked on a document asking if Mr Payne had suffered any blackouts in the last five years.
However, the court heard a number of claims he had collapsed during that time.
Miss Bain accused Payne of being "totally and utterly unreliable about his medical history". She went on: "If you had answered Yes (on the document), you would not have been allowed to drive.
"You were reckless to the safety of other people using the streets because as we have seen today you are just looking out for number one."
Mr Payne replied: "I don't want to answer that."
The QC also said: "Your selfishness has taken the lives of two young women. You could have prevented that by telling the truth."
Payne again replied he could not answer.
The inquiry continues.