What kind of Fallacy is this?
False dilemma/false dichotomy overlaying a fallacy of equivocation, which latter is: equating death of a preborn with deportation of an illegal. If death > return of an illegal immigrant, then the argument cannot be equally reversed. That equivocation of equation is the basis of the error. The secondary fallacy is a false dichotomy: while birth and abortion are obviously not a false dichotomy, as they describe an either-or condition, deportation of an illegal immigrant is a false dichotomy (i.e., they remain or they leave is a false dichotomy, in that more than those two solutions are reasonably and commonly possible: i.e., the illegal may be granted citizenship, or a green card, or a temporary work permit good for 1-3 years, or deported and/or allowed to register in a special program ahead of other legal immigrants, or some de-corrupting of said illegal's "3rd world governent" to allow more free market activity and foreign aid to reduce the poverty-motivated emigration, etc.). False dilemma is a tertiary fallacy, simply positing two choices, which is false, as death > life is >> than return to legal nation of origin > some type of non-dichotomous solution to the illegal immigrant's forcing of herself or himself against the laws of a sovereign nation-state (contrary to international law and the general laws of nation-states). NB: if one posits "deportation = death (abortion)," then there is no fallacy of equivocation; however, this equating is typically a hypocritical position--most people would choose to return to their country of citizenship, rather than affirming "being deported = being aborted," and therefore agreeing to be sent on a random basis to death camps, or returned to their nation of citizenship--if "deportation = death (abortion)." p.s. An ironic consequence, albeit given in a conservative perspective: https://www.conservativereview.com/news/mexicans-are-paying-in-blood-for-our-central-american-amnesty-policies/
You noticed how easy it was to destroy the argument. A shame that people can't just reason with one another withoit getting so bent. In an already emotionally charged topic, anytime someone says things like that, they are playing to pity, which is a dead giveaway that their argument is weak. But I would call this specific one "False Dilemma/False Dichotomy." Maybe someone else sees it differently? This line of reasoning fails by limiting the options to two when there are in fact more options to choose from. The false dichotomy fallacy fails logic by oversimplifying the range of options. "If one supports a certain abortion position, then they must support a certain immigration position." This is obviously easy to refute.