The veteran's mental health had declined after the sudden death of his infant son and breakdown of his marriage, but Ms Finney said the defence force didn't help him.
They instead medically discharged him from his hospital bed, leaving him without a job or home after 20 years of service to his country.
"Nobody is out there looking after your child," Ms Finney told the Royal Commission into Defence and Veteran Suicide on Monday.
"This family that they pretend to be is not there in any way, shape or form if you are in distress."
She said "as far as I'm concerned, they discard and destroy".
David Finney died by suicide in February 2019. There has never been a coronial inquest into his death.
Ms Finney has not been able to grieve properly because she's still seeking answers.
"Someone is absolutely accountable," she said.
"This is not something you move on from, there isn't closure."
Ms Finney spent years campaigning for a royal commission into veteran suicides, noting there were clearly systemic issues within the defence force.
She criticised the pushback against the inquiry that she received from the previous federal government, describing their actions as "disgusting".
"Veterans have been fighting for this - I'm not going away," Ms Finney said.
"Words that are often used are, we'll never get to zero suicides, and my answer to that is, but we have to try because then we'll know we've done our best."
At least 1600 Australian veterans died by suicide in the years between 1997 and 2020, royal commission chair Nick Kaldas said.
The inquiry previously heard there was a backlog of more than 30,000 veteran compensation claims made to the Department of Veteran Affairs.
Mr Kaldas noted there had been positive work to clear the backlog, but veterans were continuing to find the department's adversarial approach distressing.
"The DVA needs to start viewing itself as an agency that supports veterans, rather than simply an insurance claims processing house," he said on Monday.
The inquiry will hear evidence from Victorian government officials including premier Daniel Andrews in Melbourne sittings over the next two weeks.
Mr Andrews is expected to give evidence about how the Commonwealth and state work together on veterans' affairs.
The Inspector-General of the Australian Defence Force will also give evidence about the agency's role in ensuring accountability.
The inquiry will examine how the inspector-general's office maintains its independence while operating inside defence.
The royal commission was established in July 2021 to examine how the system is failing ADF members and veterans.
After this round, it will adjourn until November when hearings resume in Sydney.
Submissions can be made until October 13, with a final report to be handed down in mid-2024.
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