Curious about realistic reduction in nose size vs. breathing ability

I recently had a (successful) septorhinoplasty. In addition to resolving breathing issues, my hump was removed, and my bulbous tip refined. Whilst my nose is smaller, it's still large by female standards. I had asked my surgeon to go smaller. He said that he couldn't have done that without compromising the result of my breathing. My question is - is that indeed true? And if so - how are people with "petite" noses able to breathe properly? I'm genuinely curious.