Leach said deaf people have a different culture from mainstream society - they're more blunt, value-face-to-face time and have a vastly different experience of the world. Therefore they needed to be led by people who knew this first-hand.
"They prefer to employ hearing people because they have more skills, rather than upskilling deaf people," Leach told the Herald exclusively.
"They don't understand; they don't know deaf culture, habits and language. It feels disrespectful.
"We feel like we've been elbowed out of the way."
She compared it to hiring a Pakeha boss for a Maori organisation.
"You wouldn't hire a Pakeha CEO."
About 380,000 Kiwis have a hearing impairment of which 11,000 use New Zealand Sign Language as their primary form of communication.
Deaf artist Abbie Twiss said she was sick of seeing tokenism where a few deaf people were recruited so the organisation looked diverse, but such people never reaching management.
"In the hearing-led environment there's a 'hearing superiority' that deaf people really feel," Twiss said.
Lachlan Keating has been Deaf Aotearoa's chief executive for five years. He is hearing and said he had a conversational level of sign language. He used interpreters every week for complex situations.
Keating believed deaf leadership had improved under his management. He said of his 76 staff, 41 and half of his 14 management staff were deaf and over the past two years they had put 25 deaf people through qualifications.
Keating was appointed by the board of trustees who are all deaf.
"There's never been more deaf managers and deaf leaders than now," he said. Keating believed hearing chief executives were appointed "because they're the right person for the job at the time".
He said if a particular job or situation required a deaf person he would give that job to them.
Acting chief executive of Kelston Deaf Education Centre Tom Purvis, who is hearing, said about 20 per cent of their 195 employees were deaf, with a similar proportion in management.
The Auckland Deaf Society refused to comment on how many deaf people they employed or whether chief executive Fiona Brennan was deaf.
Green MP Mojo Mathers, one of only five deaf MPs in the world, said it shouldn't be left to a "tiny handful" of organisations to meet employment aspirations for deaf people.
Deaf facts
• Statistics NZ found a hearing impairment affected 380,000 people (9 per cent of the total population).
• New Zealand Sign Language is one of three official languages in New Zealand, along with English and Te Reo Maori.
• NZSL has its own grammatical structure, which enables users to communicate fully and express thoughts and emotions.
• About 11,000 deaf people use NZSL as their primary form of communication and about 20,000 people in total who use NZSL. This includes parents who use NZSL to communicate with their deaf child.