Autonomous vehicles as cognitive agents will be an important use case of artificial intelligence in modern societies. Investigating how to increase acceptance and trust, we created a self-explaining car, informing passengers before actions in virtual reality. This study investigates the attitude towards self-driving cars with data from 7850 participants. We show how gender and age affect the attitude towards autonomous vehicles, resulting in female participants being generally less trusting of overall conditions than male participants and a general decrease of acceptance with increasing age. Surprisingly, a self-explaining car providing the passenger with crucial traffic information, although it has a positive impact on trust but influences the intention of using such a car negatively. Therefore, we argue for a highly individualizable in-car communication that meets the adversarial needs of different demographic groups to enable human-machine interactions that foster safe traffic behavior and increase trust and the willingness to use such technology.