Translation:You are teaching Czech here, but you do not know it yourselves.
To speak is to make sound with your mouth. Or to be able to speak the words of some language.
To know is to have some ability. To be able to use the language.
Pretty similar, but not the same. Here I would argue that a typical use case of this sentence would be when someone told use that we don't know Czech properly. Of course he knows we speak Czech, we are native speakers, but still we may not know the proper rules of advanced grammar and orthography which must be learned and do not come automatically with being able to speak the language.
In Duolingo translations should be as close as possible and if a direct translation of a word can b used, it should be used. It is one of the rules so that the number of possibilities does not grow out of bounds. In Czech it often does so anyway.
Only to some extent. You can't say to a native Czech who wrote you a letter full of grammatical mistakes that he doesn't speak Czech. He does!
But you can tell him he doesn't know Czech.
There are simply subtle differences between knowing and speaking, they are different verbs. Especially for dead languages, which many people know, but only few of them can speak.