In its response to the Equal Opportunities Commission report Free to Choose: tackling gender barriers to better jobs, the union says teenagers would make more informed choices when they are older.
Natfhe says further education should play a bigger role in helping teenagers to choose from a greater range of careers, free from the influence of parents and their peers at school.
Kate Heasman, Natfhe equality official, said: "We share the EOC's concerns about extreme gender segregation in vocational education. If 13 or 14-year-olds are obliged to make early choices between vocational and academic paths, many will be influenced by stereotypical images and peer pressure to choose traditional vocational options.
"Young people would be better served by post-14 education, which combines academic and vocational elements, so they can later choose from many careers."
The EOC report says: "Britain is failing to provide real opportunity and choice for girls and boys entering work from school and college, despite the interest of many young people and employers in opening up 'non-traditional work' to the opposite sex."
Although women make up nearly half of Britain's workforce, many careers are regarded as no-go areas for them, it says, and the education system is channelling them towards traditionally female occupations, such as childcare. The EOC also says schemes such as Apprenticeships are not flexible enough for those with other responsibilities, such as childcare, creating a "barrier" to women.
It quotes an employer saying: "This is a job for big strong men. We don't want women coming in here with their hormones."