We can think of the theoretical implications that link crime and citizenship to get at the substance of this question. According to social contract theory, particularly as elucidated by early-modern political theorists like Hobbes, Locke, Kant, and Beccaria, a “crime” is an intentional violation of the unspoken yet mutually understood commitments that rational people make with one another in order to form civil society. In a perfectly ordered state, individuals agree to give up certain personal freedoms (theft, murder, and so on, which society generally refers to as crimes) in order that the social body can enjoy collective assurance that their fundamental civil rights will not be violated. Those individuals who commit crimes, in a theoretical sense, therefore, break the social contract that they have made with their fellow citizens and thus lose the right to be members of civil society. Kant expressed this very concisely when he said that a crime is “an infringement of public law that renders the guilty person incapable of citizenship (Emmanuel Kant, Political Writings, ed. Hans Reiss, 1991, pg. 154.)” He loses his right to citizenship precisely because he has broken the sacred vow—the “contract,” in the terminology of the early-modern period—that he and his fellow citizens agree confers citizenship on an individual in the first place.
Other authors have taken a more politicized view of this question. The criminologist John E. Pinkard Sr., for example, in his book African American Felon disenfranchisement: Case Studies in Modern Racism and Political Exclusion, has argued that some political elites have a vested interest in denying felons citizenship rights because, demographically speaking, it would work in their favor. In this view, the denial of citizenship from prisoners is an act of institutional racism, because these laws would disproportionately affect only one segment of the total American population. In 2010, according to Pinkard’s data, African Americans, who comprised 13% of the population, made up 37% of the US felon population. By removing citizenship from this group of people, the representation of the entire community of African Americans in the electorate would be disrupted. The loss of such a large fragment of the voting populace would ensure that the interests of the American black community as an aggregate would not be accurately represented in politics. This, according to Pinkard, is a form of political repression that is built into the American justice system.
You can use these theoretical justifications to think through even more reasons as to why certain people would want felons to lose citizenship.