why can't I say "Ten vlk je svůj" if the wolf is in my possession?
It's not about your possession, "svůj" refers back to the subject of the sentence. Your sentence is a non-sense, it would mean that the wolf belongs to itself.
Would that make no sense? In english that would be kind of poetic but it would have meaning. Like says, he is his own man. A statement about it's independence. Is that possible here?
It could perhaps mean what Esus already said.
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+FunFact This would mean: "The wolf is weirdo."
Why isn't "To je můj vlk" valid?
That is: "That is my wolf."
Why "tamto vlk je můj" is considered wrong?
"tamto" is neuter, "vlk" is masculine, it's a mismatch. "Tamten vlk je můj" is correct.