1. “My” will inevitably contradict with “Your” (see the article’s LinkedIn screenshot). It seems forced. Using “Your,” when appropriate, approximates a dialog between you[r system] and the user.

2. Avoid both for simple labels, tabs, and buttons.

Eventually, you will need copy that explains something to the user. When you do, you will not be able to keep your copy consistent by continuing to use "my".

"If you have questions about your account, call..."

I think the suggestion is that if you think of the design in terms of a dialog rather than a set of conventions, there are a lot of advantages. "My" vs "Your" is just an example.