Isn't the independence of the soul, only a false notion?

[How can you say in the above example that the cat does not interfere and that the rat has freedom of choosing the direction to run, when even the choice of direction of the rat is under the cat’s control? Isn’t the rat only under its superimposed false notion (ego/doership) that it is independent and it is taking its own decision, when it is actually not so. It realizes the reality only at the end when it is swallowed by the cat].

If you analyze the time of sunrise or sunset, it is a mixture of both light and darkness, which are contradicting each other. You cannot say that it is only light and you cannot say that it is only darkness. It is true that wherever light exists, darkness cannot exist and vice-versa. Yet, you cannot deny the mutual existence of both light and darkness in this situation. Similarly, the rat is having full independence since it can go to any direction to receive the heat of the fire or the coolness of water. This is the full independence of the rat because the supervising cat does not interfere with the freedom of the rat in selecting the direction. Similarly, the Lord does not interfere in your choice of selecting good or bad. Thus, there is full freedom as per the Gita (Swabhavastu Pravartate).

But the cat is supervising the selection of the direction by the rat. The supervisor does not interfere for all practical purposes. But this does not mean that the supervisor cannot interfere. If the cat wants, it can control the direction of the rat. You must distinguish between the two statements; one is “the cat does not interfere” and the other that “the cat can interfere at any instant if it likes to do so”. The first statement implies the full freedom of the rat and the second statement implies the full control of the cat. The situation reveals the mutual existence of both freedom and control without contradicting each other. Such control is also referred to in the Gita (Upadrashta Anumantaacha). This means that the Lord supervises and allows the freedom. The freedom is not real but it is an allowed freedom under the constant supervision of the Lord. The Gita mentions about such mutual existence of the two contradicting parameters (Kartaaha Mapi Sarvasya…). It is very subtle point, which is to be understood by hairsplitting analysis. It requires logical insight in depth.