Plans to expand Moor Allerton Hall Primary School by more than 200 places went before officers and education experts in the council's school organisation advisory board.
The plans would involve extending the school to a three-form entry school from September 2019.
This would increase the capacity from 420 pupils to 630 pupils over a number of years, with each intake rising from 60 to 90 pupils.
But some parents believe the school is underperforming and is too far away from the areas that need school places, while others believe it could impact on the quality of life for people living in the area.
Darren Crawley, from the council's school place planning team, said the authority was trying its best to make sure parents had enough places near to where they lived.
He added: "My view is having a school that is a mile, or a mile and a half away, is better than having a school that is two or three miles away."
The meeting was told the plans were to "remodel" a nearby pub site in order to accommodate the extra pupils.
A member of the board said: "Normally you expand a school that is good or outstanding, but this school has a challenging history."
Council officer Tracy Ward said the authority was confident the school would get its 'good' rating back.
Its most recent Ofsted inspection was in 2017, and said the school required improvement.
Leeds headteacher Sally Bolton, also a board member, said it felt like a "phenomenally short amount of time" to create extra capacity by September 2019.
A council officer responded by saying temporary buildings would be put in place if needed.
The meeting also heard from parents and people living in the local area. Saul Clayton lives in a lodge on the entrance road into the school. He said: "This will have a massive effect on us if it goes ahead.
"We have completed renovations to the property - the proposed extensions of the school will completely spoil our enjoyment of the area.
"They are now proposing to extend the school boundary so we will be surrounded by a metal fence on three sides, which would be akin to living in a prison."
He also argued that noise, light and air pollution would blight the area. He argued there was also a problem with flooding in nearby Lidgett Lane.
Andrew Kirby is a parent who lives well over a mile away from the school in Roundhay, where much of the school provision is said to be needed.
He said: "It is unreasonable to expand a school that is currently failing. This whole thing smacks of panic. Children do not need to move into a school that is failing in a different postcode.
"We put five preferences. We did not put Moor Allerton Hall down - there was so much uncertainty about what was going on - to have the school foisted upon us feels like a con trick.
"It is inconceivable to think children can walk that distance twice a day. In terms of order of preferences, people would choose Moor Allerton Hall if they had confidence in it - if it was a better school."
Chairing the meeting, Angela Cox said: "We recognise there is a need for places, and this is an extremely ambitious and complex plan with a challenging timescale.
"There would be significant highways issues that would need to be addressed.
"We are not sure that it gives parents anything to do with preference and there needs to be more work done to manage this.
"Our recommendations to executive board is a unanimous 'no'. We believe it is extremely risky."
The council's executive board is expected to make a final decision later in the year.