Mayor Lianne Dalziel told Chris Lynch on Newstalk ZB they are holding a genuine public consultation on the plans.
"I have heard people make comments that this is a slam dunk, it's a foregone conclusion, I just wanted to mention ... the Papanui Parallel cycleway from Northlands Mall to the central city, more than 80 changes were made to that."
Dalziel said she will personally go and speak to the owners of the Copenhagen Bakery.
The cycleway is expected to provide a connection for local cycling trips in the Harewood, Bishopdale and Papanui suburbs.
Street parking will be reduced to three parks outside Copenhagen Bakery on Harewood Rd.
Owner Donna Thomsen told Chris Lynch elderly customers and tradies rely on street parking when the 12 on-site parks are full.
"Of course the kids need to be safe and I do love to see bums on bikes but the democracy of the process is very disingenuous. We only got approached last week.
"This will annihilate our business."
The removal of on-street parking is a key part of the wider plan.
Councillor Aaron Keown said the exact number of parks that are expected to be removed is not known but it is "most".
Keown said the entire Fendalton-Waimairi-Harewood community board, which he is a member of, opposed the plan.
"When you hold up traffic and keep it on the road for longer, it uses more carbon so it's a bit of a farce when we claim climate change and say we're going to save the planet.
"A big chunk of the population isn't going to use the cycleways so they're [council] going to try and force them out of cars and I think the public is smart enough to know that that's the agenda that seems to be going on."
Keown said the cost of the plan, an estimated $20 million, is far beyond what the community board was expecting.