That's really an interesting quesion. Actually 不能 indentically means cannot. 我不能说汉语 actually can mean that I am not able to study Chinese because you do not have any knowledge of Chinese according to the context. Also it can mean that you are not allowed to speak Chinese according to the context, however I think that they can both be used as you cannot speaking English per see.

Hi Danny, your understanding is totally right! the example is also right! 不能= not allowed to do 不会= not be able to do

To express "I can't speak English", 我不会说汉语sounds more natural. If you say我不能说汉语, it would sound a little bit weird though we can still understand you.

不会 is exactly what u mean. 我不会说汉语 means i cant speak chinese because of a lack of the ability. 不能 means something is forbidden. for example, 你不能在图书馆里大声喧哗。