There are quite different aspects to this. Formally insults are considered "libels" (or to translate it more literally from german: violations of honour). Some things depend a lot on the indivdual circumstances and actions, some are almost universally. Insults can be expressed verbally, non-verbally and through various means of communication (text, pictures, gestures, etc..).

For example, showing a driver the middle-finger (which is the common "fuck you"-gesture), because they took your right of way, is usually considered an insult. Whereas it is not considered an insult if you and your friends do that among yourselves with a humorous intent (which also needs to be perceived humorous for all participants). Another example: dumping your softdrink over your fellow pupil is usually an insult. Calling someone "bitch" can be an insult if it's meant in a demeaning way. It is not an insult if it's meant in a friendly manner, like the "heey biaaatch" and suchlike in colloquial English.

So it really depends on the intentions behind it and the reception of the one receiving the insult.

The jurisdiction of the German Federal Supreme Court of Justice says that insults are expressions about contempt or "dishonoring" (idk if that's a good translation) towards another person.

I could write a whole lot more about this as there are even more aspects to this (e.g., how family is a special case, how you don't even need to be the victim of an insult and it could still be illegal, some "flavours" of insults which are handled by different laws and much more), but I'm too lazy to do so now. ;)

But, which is very important and to avoid confusion: You can have a negative opinion about someone and are allowed to express it. It just depends on how you express it. Opinions and insults are different things. Freedom of speech is protected in Germany, but that has limitations there, where you can really hurt someone. (Reminds me of how insults provoke similar neurological reactions as a slap in the face.)