Why is there no self in the container of the 5 aggregates?
This is the problem with mixing up ultimate reality with conventional reality. In ultimate reality, the cat does not exist. What is real is the tactile experience of the touch. That experience is an instance of the 5 aggregates arising due to causes. The experience is impermanent, unsatisfactory and non-self.

'Container' is only a concept in the mind. It doesn't exist. Sights can be sensed, sounds can be sensed, aromas can be sensed, tastes can be sensed, tactile sensations can be sensed, mental objects can be sensed. 'Container' is not something that can be sensed. So it's nothing more than a concept. It has no basis in ultimate reality. Vipassana meditation is about stop looking at the world in terms of entities and start looking at the world in terms of experiences. You cannot see the 3 characteristics in concepts.