The trouble is that 'I go to school' can also mean 'I am going, right now, in this moment'. It is old-fashioned, but still correct.
Not really, ill try to tell you why. The verb IŚĆ means TO GO, right? BUT it doesnt explain how you go, just that you go. Now, the problem is when in english you say I GO BY BUS, the verb is GO but in polish TO GO by a bus, car, etc is JECHAC/JEŹDZIĆ (to go by any means of transport) If you think that you are going on foot (to go walking) the verb can be CHODZIĆ if you do it repeatedly, like every week, day, etc. Thats why you cant say I WALK TO SCHOOL because that particular sentece in poland implies that you go regurlarly since you dont hace any word that says otherwise (like -I WALK TO SCHOOL NOW-) In the last case you can write Idę do szkoły teraz, meaning I go (walking) to school now, or Chodzę do szkoły, I go (walking) to school (regularly). You could say Idę do szkoły piechotą (I go to school by foot) but the same problem presents as in Idę do szkoły without the NOW. Is difficult to understand because in polish the verb to walk doesnt exists.
After saying all this, if the situation is right, you just can simply not pay attention to it and translate it like I walk to school and everyone will understand anyway :)
why is school in the genitive case? I would think going to school (depending on exactly what you're trying to say) would be either dative or, more likely, accusative, and this isn't clear to me
I think 'I go to school' is also a fair translation. I live in Poland and its used even if the correct tense is Chodzę do szkoły
In this context "I walk to school" does in fact mean "I attend school", although the more literal translation of the latter would be "Uczęszczam do szkoły".
Why is 'I go to school' wrong? Is that not the same as 'am going to school'?
Not exactly, because Verbs of Motion do show the difference between Present Simple and Present Continuous. So "idę" should translate only to "I am [going/walking]".
However, there are some nuances connected with idiomatic usage, that I don't understand well (but I was explained by a native), that make "I go" an acceptable answer if the sentence is about going to school. That's the only exception that we're aware of. Just an exception.