It's not logically consistent. You're claiming that p implies not p

Oh come on, the claim is that safe (p) <-> !p, which is a bit different. Attack the actual claim.

@pmalynin, you forgot the safety variable.

  p | q | p ∧ q → ¬q
  --+---+-----------
  T | T | F         You can't be safe and own a gun.
  T | F | T         You can be safe and not own a gun.
  F | T | T         You can be unsafe and own a gun.
  F | F | T         You can be unsafe and not own a gun.

@rwjwjuwjudf, logical implication is correct - logical equivalence leads to this trainwreck:

  p | q | p ∧ q ↔ ¬q
  --+---+-----------
  T | T | F         You can't be safe and own a gun.
  T | F | F         You can't be safe and not own a gun.
  F | T | T         You can be unsafe and own a gun.
  F | F | F         You can't be unsafe and not own a gun.

Nice analysis! I was thinking safety is a function equivalent to negation. But I agree if safety and gun ownership are separate variables.

  p | safe (p) | ¬p | safe (p) ↔ ¬p
  --+----------+----+--------------
  T | F        | F  | Owning a gun is unsafely owning a gun.
  F | T        | T  | Not owning a gun is safely owning a gun.

I think this is the original reason why it's confusing, because the sentence "not owning a gun is safely owning a gun" is highly unintuitive. There is a contradiction because safely owning it conflicts with not owning it.

edit: I think we can legitimately fix the confusing sentence to read "not owning a gun is safely not owning a gun".

Safety as a negation would be an xor operation, which leads to the wacky logic. Both of you are right though, I was probably far too generous in treating @minikites's use of the word "is" as a logical implication instead of the logical equivalence that you suggested. The resulting logic leads to conclusions that both support and refute the likely intent of the original statement. So either the logic is broken or the intent is :) If only @minikites had used the word "maybe" instead of "is"... the weaker position would have been supported with a logically consistent argument.

I think the original expression was poor, it could perhaps be paraphrased as "gun safety is an oxymoron".

That still leaves five words to debate about, to quote a very sly fellow "It depends on what the meaning of the word 'is' is." I'm pretty sure we could distill the argument to the point where we find ourselves debating the finer points of chaos theory.