Threats aren't illegal because of their information content, they're effectively evidence of intent to commit violence. It's like confessing to a crime. You're being punished for the crime, not for the admission, but you admitting to it sure makes it easier to prove.
You and the parent both made good points. In Germany a swastika might be seen as more of a direct threat of specific action than other places. That makes it more sensible to classify as a threat.
That's the argument authoritarians use when they want to censor something. The problem with it is that it proves too much. Do we also get to apply it to symbols of communism because of the millions of people who died under Mao, or the US flag because of slavery? What about that book Marx wrote that led to all the horrors under the USSR; can't displaying books also be symbolic?
You don't want the government to have the power to decide things like that. It's better that they censor nothing.
