In order to mean "to teach", "å lære" either needs to have the person/people being taught as an object, or a little help from the adverb "bort".
Jeg lærer norsk. = I am learning Norwegian.
Jeg lærer meg norsk. = I am [learning/teaching myself] Norwegian.
Jeg lærer henne norsk. = I am teaching her Norwegian.
Jeg lærer bort norsk. = I am teaching Norwegian. (more on the colloquial side)
Jeg underviser i norsk. = I am teaching Norwegian. (typically in a school setting)
"You can teach to read well" sounds unnatural in English and it doesn't really make sense. It feels like there should be a subject between "teach" and "to", for example "you can teach her to read well". So it's probably not correct as a translation because it's bad/unnatural English.
The point remains that lære translates both into "teach" and "learn", and we should not be guessing what the correct one is using as a proxy how natural the result sounds in the target language. Also, as a native English speaker, I don't see anything wrong at all with "You can teach to read well".
The answer is more that English has two words, one meaning 'to gain knowledge' (i.e. 'to learn' from a teacher or from an experience etc.), and one meaning 'to give knowledge to someone else' (i.e. 'to teach'). But Norwegian has just one word 'lære' that does both jobs in different contexts. You can see how that works in some English dialects and in dated speech where it's correct to say something like "Sweet prince, you learn me noble thankfulness", where Claudio is saying that Don Pedro has taught him noble thankfulness.
As a native Brit I think "you can teach to read well" sounds very odd! But it means that the teaching is good, not the reading: you can teach [whatever it is] well. If it is the quality of the reading being described then you need to mention the person that is being taught. Eg: you can teach the boy to read well.
I am not using that as a proxy. I am not denying 'lære' means both 'teach' and 'learn'; of course I know this. I'm not saying one meaning is more correct than the other. But surely you can't deny that not all words in another language which have multiple translations can always be translated as any of those options into the other language? It doesn't mean that such a word doesn't still carry those other meanings, but there are of course going to be instances in which one translation will not make sense in the language being translated to. This, honestly, is one of those instances. I must say that 'you can teach to read well' sounds very unnatural to my ears. It does not make sense to say this. In my opinion, it sounds clumsy and just wrong. 'You can teach someone to read well', or something like that, would be better.
You need to use the Norwegian character æ for 'lære', and å for 'å lese'. On my laptop/phone I can just hold down the vowel key and options pop up for me to select foreign characters, but it varies depending on what type of phone/computer you have. If you're using a PC, you will have to learn the alt-codes.