The row started when Mr Shearer asked Mr Brownlee about why he thought New Zealand trainers would make any difference when the United States had spent 10 years in Iraq and $20 billion training Iraqi forces who had fallen over when put to the test.
Shearer: "What makes you so sure New Zealand will do a better job that the US military did who spent a decade there?"
Brownlee: "I think the derisory nature of your question is something I ignore for a start ... I just think the way you are putting that is pretty pessimistic and somewhat disrespectful of the New Zealand effort there.
"These are real people, real New Zealanders who are on the ground trying to make a difference. They are responding to Government policy ... trying to degrade the efforts of the soldiers in the field I think is pretty reprehensible."
Shearer: "I take real exception to that. You are here to answer and come before a committee any question about why we have got people in harm's way and you have the audacity to turn around and ask me that somehow I'm saying I'm being derisory about our own people out there. I'm not."
Brownlee: "Yes you were."
Shearer: "What I would like to know and New Zealanders would like to know is why they are there and whether in fact they are able to do the job because that is about Government policy and if the Government policy is flawed and actually bankrupt then frankly they are there for absolutely no good, no matter how good they are."
The pair clashed over whether there were any targets of the number of troops New Zealand would be training in the two-year joint mission with Australia.
Mr Shearer said he found it incredible that Mr Brownlee did not know a target but was able to say 1200 Iraqi recruits would have a passing out parade soon -- graduates of the coalition of countries training, not just New Zealand.
Mr Brownlee said the US had set a target of 24,000 Iraqis to be trained by the coalition but he could say what the New Zealand target was but it would be high numbers.
Shearer: "I find it incredible that you cannot tell us after $65 million and 143 staff what they are actually meant to be doing. What have you told them to do other than train high number of people." He later clarified it was 1800 over two years.
Brownlee: "Calm. Just calm. Get serious. We've got 16 trainers there. The rest are there to ensure the entire mission goes well ... don't rush to overstate thing with your excited approach to things."
The pair clashed again when Mr Brownlee was questioned about the photographs of illegal fishing boats taken by the HMNZS Wellington in January -- Labour thought the Navy should have boarded the boats, not just photograph them.
Mr Brownlee thought a smile by Mr Shearer at one of his answers amounted to scoffing.
"I'm sorry by that cynical laugh there," Mr Brownlee said. "That is the classical armchair general. Not there. Wasn't there. Looked at a photo in the paper and then makes a proclamation about the worthiness or otherwise of the efforts of the crew.
"Frankly they did a great job, they got the evidence and now we're getting the prosecution."