Not losing gun rights will not cause the losing of children. I would go so far as to argue the opposite. GGs with guns at Sandy Hook would have caused FEWER deaths among the children.
I blame the anti crowd for the scale of the carnage (and actually the very existence of that carnage) at Sandy Hook.
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What jumped out at me the most is what I would (possibly not accurately) describe as a false dilemma. The statement seems to assert that the choice is either guns or children - obviously that is not the case. There are more than these two options, and they are non-exclusive. The suggestion that one must chose one or the other, and that the options are conflicting, is false.
The statements also seems to improperly generalize the "sides" of the issue. It imposes that one is either a gun activist, or a mother, and that the two groups are pinned against each other. In actuality, though, many mothers are gun activists, and I'm sure that the vast majority of them are both for their guns and their children. Perhaps even for their guns because they're for their children. I'm not sure how to identify this though as any particular logical fallacy, perhaps someone can help identify. It may be several.
http://en.wikipedia.org/wiki/Base_rate_fallacy
http://en.wikipedia.org/wiki/Fallacy_of_the_single_cause
http://en.wikipedia.org/wiki/Moralistic_fallacy (eg "valuing guns above children is wrong, therefore gun control will win").
http://en.wikipedia.org/wiki/Appeal_to_motive
The number of fallacies kind of depends on how you interpret the argument. If it's just making a prediction about whether gun control or gun rights will win, which is the weakest reading, then it contains relatively few fallacies. It seems implicit that it's also arguing for gun control on a moral basis, though. In that case you can add straw man, since parents (ostensibly) care about their children as children, whereas gun owners care about guns less as things-in-themselves than because of their functions (preservation of life and liberty, acquisition of food, recreation, etc). So the comparison would really be more like:
Parents care about losing their kids
Gun owners care about losing their rights, freedoms, lives, food sources, and hobbies.
I think this sort of excluded "why" is maybe its own unique kind of fallacy. Maybe it should be called the politicians fallacy. When arguing to ban, tax, or regulate something, it is treated purely as a thing-in-itself with no actual function or material benefit.
How many logical fallacies can you find in the attached photo?