In a personal interview with blog Humans of New York, she said she was told at the admissions exam she should forfeit her place so a man would not be drafted and sent to Vietnam.
She also revealed that as a young woman she learned to "control her emotions".
The Democratic candidate was criticised this week by the Republican party chairman for not smiling enough.
Reince Priebus was accused of sexism when he said Mrs Clinton had appeared to be defensive and angry when she was questioned by veterans at an event in New York on Wednesday.
Her Republican rival Donald Trump has also criticised her looks, saying he does not "look presidential" enough.
How do you 'look presidential'?
On the Humans of New York Facebook page, Mrs Clinton said she felt pressured into not going through with the law school exam.
"My friend and I were some of the only women in the room. I was feeling nervous. I was a senior in college. I wasn't sure how well I'd do. And while we're waiting for the exam to start, a group of men began to yell things like: 'You don't need to be here.' And 'There's plenty else you can do.' It turned into a real 'pile on.' One of them even said: 'If you take my spot, I'll get drafted, and I'll go to Vietnam, and I'll die.' And they weren't kidding around. It was intense. It got very personal."
She said that she can sometimes be perceived as "cold or unemotional" but she had learned to control her emotions when she was younger.
"That's a hard path to walk. Because you need to protect yourself, you need to keep steady, but at the same time you don't want to seem 'walled off.'"

Austen Harrison suffered fatal head injuries at the Hugo Boss shop in Bicester, Oxfordshire, in June 2013.
Hugo Boss UK pleaded guilty to breaching the Health and Safety at Work Act and Management of Health and Safety at Work regulations.
Sentencing is due to take place at Oxford Crown Court on 19 June.
Austen, of Crawley, West Sussex, had been playing with the unfixed steel-framed fitting-room mirror which toppled on to him while his father tried on a suit in the shop at the Bicester outlet village.
He underwent an emergency operation to relieve pressure on his brain but died four days later in hospital after life-support was switched off.
At a hearing at Banbury Magistrates Court on Tuesday, Barry Berlin, prosecuting on behalf of Cherwell District Council, requested the case should be sentenced at Oxford Crown Court where fines of Â£100,000 or more could be imposed, rather than the Â£20,000 possible at a magistrates court.
An inquest jury at Oxford Coroner's Court earlier this year returned a narrative verdict.
Austen's death was an "accident waiting to happen", the coroner said.
Hillary Clinton has said she was singled out as one of the only women applying to go to Harvard law school.
[NEXT_CONCEPT]
A designer store has admitted health and safety offences following the death of a four-year-old boy who was crushed when a 120kg mirror fell on him.