You haven't misunderstood it! You're just coupling cellular respiration with photosynthesis, which on the surface seems to balance to net zero -- 6 CO2 molecules and sunlight create 1 glucose molecule, and we break down 1 glucose molecule for energy and generate 6 CO2 molecules.

There's one big factor though which isn't immediately obvious, and that's the rate of reaction. The chemical equations say nothing about how many molecules are consumed per second. In order for the net CO2 to be zero, they'd need to consume and generate CO2, respectively, at the same rate, which isn't the case.

It's actually a really good thing, because photosynthesis happens faster. Plants are net negative CO2 because of that. What we'd need to complete this comparison now is how much CO2 a human generates by existing, and we can determine how many plants are needed per human to have the same net CO2.