Does “I swear I care” mean someone actually doesn’t care?

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so I'm new here, & I didn't realize that the forum changed the wording of my question before I posted it. my original question was, "if someone tells you, "I know it feels like I don't care, but I swear I do," does that mean that really do care, or that they just want you to believe that they do?"

Does “I swear I care” mean someone actually doesn’t care?
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