Why does this not become radioactive?

You are correct that alpha decay has the possibility of changing atoms into atoms of other elements, but beta decay does not have this capability. The reason is that while alpha decay is an alpha set, consisting of 2 protons and 2 neutrons, beta decay is simply an electron (or positron, but that is beyond the scope of this discussion). An element is defined by the number of protons in the atom. A varied number of neutrons will be an isotope of the same element, and a varied number of electrons will be an ion of the same element. The majority of an element's properties come from the number of protons.