The law never states that you are required to carry your ID. It states that you are required to own one.
If you do not carry it with you, and have no why for them to identify you in a way that you can be looked up, e.g. because you have your ID number in your password manager, the police can summon you to the station, or escort you home or a variety of other protocols.
The police like to convince you otherwise, because it makes their job easier. When children are taught about their ID in school, this is often accompanied by a police official. As you can see in the law itself, this is not true.
However, this only applies to German citizens, and EU citizens, if you are in Germany on a visa or any other type of scheme, you are in fact required to carry you ID and documents with you at all times. In that case not carrying an ID is actually an offense with harsh punishments. In reality most of these situations are handled like with normal citizens though.
That seems like a distinction without a difference.
If you’re required to have it and present it on demand, then almost everyone will carry it, and the tiny minority not carrying their card will be automatically suspicious.
It’s a very short step from there to simply requiring that it be on your persons.
If you do not carry it with you, and have no why for them to identify you in a way that you can be looked up, e.g. because you have your ID number in your password manager, the police can summon you to the station, or escort you home or a variety of other protocols. The police like to convince you otherwise, because it makes their job easier. When children are taught about their ID in school, this is often accompanied by a police official. As you can see in the law itself, this is not true.
However, this only applies to German citizens, and EU citizens, if you are in Germany on a visa or any other type of scheme, you are in fact required to carry you ID and documents with you at all times. In that case not carrying an ID is actually an offense with harsh punishments. In reality most of these situations are handled like with normal citizens though.
Edit: improve formatting