Cases are something that you will meet everywhere in the German language. Basically every type of word can be affected by declension, also numerals and substantivised verbs. Verbs can require Dativ, Akkusativ or both. For example, "antworten" requires Dativ: Ich antworte *ihm*. "sehen" requires Akkusativ: Ich sehe *ihn* "geben" takes two objects, one in Dativ, one in Akkusativ: Ich gebe *ihm* (Dativ) *ein Buch* (Akkusativ). Many verbs require that the objects are connected to the verbs with certain prepositions. If you study German you'll have to learn the case(s) each verb demands. For each verb, you will also have to study the preposition needed to connect the verb to the object. Also those who study English have to learn this, it's not a quirk of German. Something similar can be said for Russian, by the way.

Well, the simplest suggestion that comes to my mind is 'just don't think about it at all!' And here is why: I don't believe that this kind of grammar rule will help you in anyway. Because the native speakers do that right because their exposed to it all their life. And unless you're a student of German studies and aim for the D level, it's not for you. It's for people who are really into linguistics and wanna be an academic in this area. But it will not help you to improve your language skills (aka communication skills. There are studies showing that.) If you really wanna (intellectually) understand why you use in a certain situation this or that you have to understand that there is not THE Dativ but a whole bunch of them. And mortals don't want to go that road. Because like I said and I repeat, it will not improve your communication skills. Here is what you do: In the article she says "...because most of the time it is the only form that exists." I would focus only on that. So, take a text or a German book and read it. Everytime you come across a mich/mir, dich/dir mark it and the verb with colors in the same way as the author did. And let your brain take note of it. When you finish a whole book doing it under the condition that you understand the book. You will probably have no problems with it anymore. Like the native speaker you exposed yourself to it enough. greetings Tobi