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I find it remains one of the English language's worst shortcomings that "I empathize with you" and "I did something wrong and wish to apologize" both take the form of "I'm sorry".
It's not hard to figure out. "I'm sorry" means "I am feeling sorrow."
If you don't feel sorrow, you aren't sorry.
@BatElite And apology means a justification in defence:
@BatElite I've stopped using "I'm sorry" for the former. I explicitly use "sympathies" for that. We have the power to disambiguate our language. We just need to start doing it.