Heretaunga Intermediate School principal Michael Sisam said the Super Six was intended to promote maximum participation.
"Girls play sevens, boys play fifteens," Sisam said.
"The current structures state that girls play in girls' tournaments and boys play in the boys' tournaments."
Taradale Intermediate principal Rex Wilson said the "structure" was there for a reason and would not be changed when the competition was already under way.
"The structure of the competition was organised not for any individual student, but the majority.
"It is a gender-based structure to enable maximum participation especially from girls.
"We have found [in the past] if it is a mixed-gender, boys will dominate.
"The rules of the competition were established last year and it is up to the integrity of the people participating to maintain them."
Sisam said the schools were not opposed to making changes, but not until 2020.
"Any change is subject to advanced discussion and agreement across all intermediates.
"The sports committee does not want to jeopardise the current team structures as this may disrupt the ability of some of the teams to play."
The coach of the team Andy Lovatt told Stuff the 21 boys in the squad would either play in the tournament and forfeit any points, or would not play at all.
Havelock North Intermediate principal Julia Beaumont said they would support the team if they chose to boycott in protest.
"It is important to question when situations seem to be unfair, and also important that students learn the processes by which to have their voices heard," Beaumont said.
"In this instance with the rugby game next week, we will support the voices of the rugby players and their parents in how they choose to participate."
Briar has played since she was 5, in mixed teams, and more often than not as the only female. She also plays for the Tamatea club.
Her father Dean, the assistant coach of the team, told Stuff she was "quite upset" when he informed her she may miss her chance to play in the tournament.
"She asked me why, and I had to tell her someone thought girls shouldn't be in the team. It goes against everything me and her mum have told her in the past," he said.
Sport Hawke's Bay chairman Damon Harvey says that the decision made has no consistency with the general ruling.
"She can play club rugby and for the Ross Shield which is Hawke's Bay's oldest traditional rugby tournament, so why can't she play in a school tournament for her team?"
He commended the attitude of the rest of the boys in the team.
"What the boys have done is fantastic, not only have they stood up for something like this but they have backed their teammate whatever happens.
Harvey says forcing Briar to play sevens because she was a girl was not in her best interest.
"Fifteens and sevens are two very different games and if she plays fifteens then it's a different world having to turn around and play a different game and different teammates."
Harvey said he hoped the team did take to the field, whether they get the points or not.
Sports Minister Grant Robertson on Wednesday backed Briar playing.
"I think most New Zealanders would want Briar to be able to play with her teammates in a team she's been in all year," he told reporters.
"I really hope a solution can be found to make that happen ... They deserve a chance to play in the tournament together."
In Hawke's Bay, girls can play in mixed teams until high school, or Grade 12 in the club system, at which point they play in female teams.
Mavis Mullins, who was the first woman appointed to the HBRFU board, said it was disappointing to see a young girl not being able to play rugby for her team.
"It does seem hypocritical that she can do this through the week and come to this tournament and they deem it not appropriate," Mullins said.
Although she didn't know much about the case she said it was a missed opportunity to make a statement of promoting diversity in sport.
"It could have been a real cause for the school to make around women and girls in sport," Mullins said.
"But this is a real opportunity to be proactive and make a change for the future."
A statement issued by the organisers earlier on Wednesday said there were health and safety issues as "boys can be bigger, stronger, heavier and faster".
"By allowing students of one sex to play in a team of another sex for these one-off tournaments sets a precedence [sic] that could see boys who play in a mixed netball/hockey team play for their school's girls' netball/hockey team [at the tournament] or vice-versa.
"It could remove the need for separate sports, therefore meaning less students able to play," the statement said.
