This is what is called the "verb government". Different verbs use different government, i.e. they require nouns to have different cases and prepositions. When learning a verb, you always should ask for some examples how it is used. The same is in English. Why do we say "I hear music", but "I listen to music"? - No answer, that is the verb government.
Учить <кого-то> (Acc.) <чему-то> (Dat.). : Он учит меня (Acc.) русскому языку (Dat.). That is how it is used. Here, the person being taught is a direct object, and the subject being taught is in dative.
Объяснять <кому-то> (Dat.) <что-то> (Acc.).: Он объясняет мне (Dat.) русский язык (Acc.). Here, the subject being explained is a direct object, and the person to whom it is explained is a recipient. It is similar to English somehow: He explains Russian to me.
Проходить <что-то> (Acc.) literally means "to pass something". Colloquially, it is often used in the sense of "to learn a topic". Literally, you "pass" the topic so that you are ready to learn the next one. That is why we use it with "с нами" (with us): мы с вами проходим новую тему (We are "passing" a new theme with you).