The tax code makes a bright line out of the distinction between income and capital that is, economically speaking, quite fuzzy. Depending on your need for liquidity and your means of acquiring it, it might not be really there.
Not a particular trustworthy site, but whatever:
[0] https://www.thebalance.com/how-to-use-the-zero-percent-tax-r...
That distinction exists for a reason.
Since, as you say, the corporation is legally distinct, whether I own the whole corporation or just part of it is neither here nor there. My objection is the same, which is that there are two tollgates between me and what I see as my share of the income.
Australia's corporate tax system allows for "franking credits". Shareholders receive these from companies based on their proportional ownership. The income tax paid by the corporation may be offset against the income tax owed by shareholders.
Unsurprisingly, Australian companies are much more likely to pay dividends.
I am happy to make the normative statement that any tax code that creates such an incentive probably is badly designed, though.
If you were not actually arguing along these lines and were merely correcting his terminology without rebutting his main point, I would have expected you to preface your comment to this effect, e.g., "Not disputing your point, but technically this doesn't qualify as 'double taxation' because...".
Apologies if I've misinterpreted.