A tree is free when it is allowed to live to its fullest potential as a tree. An animal is free when it is a permitted to live true to its potential as an animal. If we were to mix it up and provide an animal with the all the needs of a tree, or a tree with the freedom of a movement of an animal, either one would not be considered free.
Same is true for people. The true expression of our freedom is when we are able to live up to our G-d given talents and abilities.
Jewish people are endowed by G-d with a soul that has a unique spiritual and G-dly capacity, it follows then, that our true freedom includes the ability to tap into and express that part of ourselves.
Torah and Mitzvot are G-d given tools that enable us to express and maximize that spiritual capacity of our souls.