Intellect is distinct from intelligence. Intelligence MAY be influenced by genetics, although the degree to which it can be has never been discovered, and there is a school of thought that all humans share the same basic threshold for mental capacity which can be reached given proper nurturing (and excluding serious defects in the brain, which obviously can be passed on genetically).
But intellect is the practice of using one's mental capacity. That requires a conscious choice. Plenty of intelligent people refuse to think. That is also a choice. Likewise, someone who is born with aggressive tendencies can choose whether to act on them or not (unless, as I said, one is arguing from a deterministic perspective, which I do not).