1 (Premise) Sarcasm is a good and wholesome form of argumentation, everybody knows this, and anyone who denies this is being clearly and blatantly sarcastic
2 (Observation) The author appears to argue that sarcasm is a bad and unwholesome form of argumentation
3 (Deduction, from 1 & 2) The author exhibits clear and blatant sarcasm
4 (Adduction, from 3) The overall tone of the author is sarcastic
5 (Obseration) The author appears to argue that Lists of Reasons is a bad and unwholesome form of argumentation
6 (Inference, from a List of Reasons that derive from various combinations of 1, 2, 3, 4, and 5) Lists of Reasons is a good and wholesome form of argumentation
We'll just skip on past the observation that your post is basically a list of examples and get right to it:
First, it is not correct to say that providing examples of a proposition does "nothing" to establish the truth of that proposition. Consider the alternative, where I advance a proposition, you challenge me to provide an example, and I cannot. That would surely be evidence against my proposition, and the negation of evidence against a proposition must necessarily be evidence in favor of it. Now, admittedly, the strength of the evidence isn't necessarily symmetrical (see: Raven Paradox), but often just getting your interlocutor to concede the existence of a phenomenon, for which an example _is_ logical proof, is an intermediate goal of an argument. (Why, then, do we list multiple examples? Usually just to head off the rhetorical dodge of claiming that a proffered example is unique and therefore dismissible as an aberration.)
Beyond that, you seem to take an unnecessarily pedantic view of argumentation by refusing to consider unstated, implicit premises. When you offer examples as an argument for a proposition, you are including an implicit premise that the examples are representative of all the examples that might be given, that you haven't cherry-picked favorable examples. Your opponent doesn't have to accept that premise, of course, but if they don't, then it's on them to rebut it [1]. In your immigrant example, people do just that, citing crime statistics as proof that the cases offered as examples are the exception rather than the rule.
Your death penalty example is particularly interesting because it's a case that I alluded to above, where simply establishing the existence of a phenomenon is almost enough to win the argument. Establishing that in practice the death penalty causes some innocent people to be executed puts death penalty proponents in the position of having to argue that executing a few innocents is an acceptable price to pay for being able to execute the guilty. In my experience, very few people are willing to even attempt this argument. Even the few that do have an uphill struggle because the marginal benefit of execution over life-long incarceration is so small. In this case, it appears that the examples don't even have to be all that representative to be convincing.
Finally, regarding sarcasm, I'm not sure it belongs in this discussion at all. Sarcasm isn't an argument; it's a mode of presentation for an argument. Good arguments and bad arguments alike can be presented sarcastically. In American culture, sarcasm, at least when directed at a stranger, usually connotes contempt, so on that basis it might not be a good choice for productive discussion. However, there is nothing at all to prevent a good argument being made in a sarcastic voice.
[1] Offering an implicit or explicit premise that you know, or should know, has been previously rebutted elsewhere is a prime example of a "bad-faith argument", and an essential feature of the "Gish Gallop" style of argumentation.
1 (Premise) Sarcasm is a good and wholesome form of argumentation, everybody knows this, and anyone who denies this is being clearly and blatantly sarcastic
2 (Observation) The author appears to argue that sarcasm is a bad and unwholesome form of argumentation
3 (Deduction, from 1 & 2) The author exhibits clear and blatant sarcasm
4 (Adduction, from 3) The overall tone of the author is sarcastic
5 (Obseration) The author appears to argue that Lists of Reasons is a bad and unwholesome form of argumentation
6 (Inference, from a List of Reasons that derive from various combinations of 1, 2, 3, 4, and 5) Lists of Reasons is a good and wholesome form of argumentation
"You say we should have the death penalty. But what about Carlos DeLuna, Ruben Cantu, and Larry Griffin who were executed despite being innocent?"
i think this one is basically legit on a reasonably charitable construction? the pretty clear implicit argument being
1. the criminal justice system sometimes punishes innocent people
2. we will never be able to categorically prevent this
3. since the criminal justice system will always sometimes punish innocent people, the punishments inflicted should not be irrevocable
4. the death penalty is an irrevocable punishment
C. so the criminal justice system should bot impose the death penalty
We'll just skip on past the observation that your post is basically a list of examples and get right to it:
First, it is not correct to say that providing examples of a proposition does "nothing" to establish the truth of that proposition. Consider the alternative, where I advance a proposition, you challenge me to provide an example, and I cannot. That would surely be evidence against my proposition, and the negation of evidence against a proposition must necessarily be evidence in favor of it. Now, admittedly, the strength of the evidence isn't necessarily symmetrical (see: Raven Paradox), but often just getting your interlocutor to concede the existence of a phenomenon, for which an example _is_ logical proof, is an intermediate goal of an argument. (Why, then, do we list multiple examples? Usually just to head off the rhetorical dodge of claiming that a proffered example is unique and therefore dismissible as an aberration.)
Beyond that, you seem to take an unnecessarily pedantic view of argumentation by refusing to consider unstated, implicit premises. When you offer examples as an argument for a proposition, you are including an implicit premise that the examples are representative of all the examples that might be given, that you haven't cherry-picked favorable examples. Your opponent doesn't have to accept that premise, of course, but if they don't, then it's on them to rebut it [1]. In your immigrant example, people do just that, citing crime statistics as proof that the cases offered as examples are the exception rather than the rule.
Your death penalty example is particularly interesting because it's a case that I alluded to above, where simply establishing the existence of a phenomenon is almost enough to win the argument. Establishing that in practice the death penalty causes some innocent people to be executed puts death penalty proponents in the position of having to argue that executing a few innocents is an acceptable price to pay for being able to execute the guilty. In my experience, very few people are willing to even attempt this argument. Even the few that do have an uphill struggle because the marginal benefit of execution over life-long incarceration is so small. In this case, it appears that the examples don't even have to be all that representative to be convincing.
Finally, regarding sarcasm, I'm not sure it belongs in this discussion at all. Sarcasm isn't an argument; it's a mode of presentation for an argument. Good arguments and bad arguments alike can be presented sarcastically. In American culture, sarcasm, at least when directed at a stranger, usually connotes contempt, so on that basis it might not be a good choice for productive discussion. However, there is nothing at all to prevent a good argument being made in a sarcastic voice.
[1] Offering an implicit or explicit premise that you know, or should know, has been previously rebutted elsewhere is a prime example of a "bad-faith argument", and an essential feature of the "Gish Gallop" style of argumentation.