An image from what-exactly-happens-to-the-signals-hitting-a-common-mode-choke doesn’t quite look right.
In respect of the first part, inductance \(L=\frac{\phi(i)}{i}\) so if the windings are equal, half the total current flows in each winding and each contributes flux due to i/2, total current is i, total flux is twice that due to i/2, so the inductance of the parallel equal windings is the same as if i flowed in a single winding, ie L of the combination is the same as the inductance of each of the equal windings alone.
In the second case, if there is zero flux leakage, it is true that the inductance of the combination of series opposed equal windings is zero. In the case of the cores used for common mode chokes flux leakage varies from less than 1% to over 50%… so the general statement is a bit naive in this application.
Both of these are very easily demonstrated by simple experiment. In fact a measurement of L with series aiding and series opposing connection is a classic way to find the flux coupling factor.
A few years after the ‘information’ was posted, it has not been questioned much less called out as wrong. So given that the understanding of inductance seems lacking… what credibility does the article have when it includes this?