Kudos to Duolingo for attention to detail.
I've been trying "may" in place of "can" all over the place, and so far everywhere I expected it to be accepted, it has been accepted.
I chuckled to myself as I tried it here, and "animals may not speak" was properly rejected. :-)
Should नहीं always go after the verb (बोल in this example)? That makes sense if नहीं सकते is the literal translation of cannot (or can not according to Duo). Thanks!
It can go before or after. I believe before is more common, and that it could be considered the "default" in some sense. When नहीं is placed after, it adds a more or less subtle emphasis to the verb. (Whereas when it comes before, the emphasis is on नहीं, the negativeness as opposed to positiveness.)
Why did the authors of Duolingo choose to use this ordering? I imagine some of their decisions were unconscious. As native speakers, that's actually OK in the sense that we get expressions that "sound right" rather than ones that always show obvious grammar rules.
I speculate that this sentence was conceived in a head-space of, say, a conversation about animal communication. The speaker has no reason to state the obvious, that "Animals cannot speak" (neutral emphasis), but rather has some reason to re-emphasize that trait: "Animals cannot SPEAK."