Personalized adaptation technology has been adopted in a wide range of digital applications such as health, training and education, e-commerce and entertainment. Personalization systems typically build a user model, aiming to characterize the user at hand, and then use this model to personalize the interaction. Personalization and user modeling, however, are often intrinsically at odds with each other (a fact some times referred to as the personalization paradox). In this paper, we take a closer look at this personalization paradox, and identify two ways in which it might manifest: feedback loops and moving targets. To illustrate these issues, we report results in the domain of personalized exergames (videogames for physical exercise), and describe our early steps to address some of the issues arisen by the personalization paradox.