I wonder if the problem that Anja discovered concerning "My" vs. "Your" is really just thoughtlessness or if the term has deliberately been chosen. In any case, the decision should consider the following problems of My vs. Your:

In distinguishing the confusion-prone concepts of
a) personalizing a portal for oneself, and
b) customizing a portal webpart for a targeted audience,
terminology emerges to use
- "MySite", "My links", etc. for case (a), while using
- "Links for you", "News for you" in case (b).
(Unfortunately, in dotLRN documentation the difference between personalizing and customizing is different). Mixing up My and You will completely confuse end users and, even more, course admins who sometimes take on both roles.