Why the view "I am the owner of my karma" not contradict anatta?
This is how you practice equanimity (upekkha). It's the one of the four divine abodes. Just like in Metta(loving-kindness) meditation where you say "may I/my parents/relatives/friends be happy, well, free from suffering etc.", Upekkha meditation is also practiced at a conceptual level. 

The purpose of Upekkha meditation is to cultivate equanimity in the mind. It does not lead to realization of Anatta nor enlightenment unless you turn it into Vipassana at some point.

Anatta is at the level of ultimate reality. That is for advanced practitioners of Buddhism. Trying to teach Anatta to everyone regardless of their mental maturity will not be productive as many will endup being more confused than they already are. That's why there are teachings in Buddhism that help you develop the mind at a conceptual level where you are familiar and comfortable. It is important not to mix up these teachings with the teachings of ultimate reality.