The teaching of this verb form in this way is not limited to Russian, nor is it limited to Duo.
нравиться is just like gustar in Spanish, piacere in Italian, and plaire in French - they all mean "to please" - yet in all the modules, they are taught as "to like", which causes an awful lot of confusion.
It seems like a teaching device from centuries ago which has managed to survive despite the fact that it is SO much easier to understand if you just say "The thing pleases me" rather than "I like the thing".
Once you've learned what it actually means, it is simple to switch to the English idiom of "liking" something.
I think Duo is simply trying to prevent learners from overusing "любить" in Russian. You use "нравиться" for saying you like a movie, a song, etc. To say "This movie pleases me" sounds odd -- hence the translation with "like" in this exercise to reinforce the like<-->нравиться connection.
You don't need to contort one language to understand the grammar of another. And getting into the habit of doing it is ultimately counterproductive to your learning to use that other language.
And, BTW, "this plan is pleasing to me" corresponds to the Russian "этот план радует мне глаз/мне приятен/доставляет мне удовольствие", and all these variants are of a slightly different meaning and/or mood than the neutral and easy-flowing "мне нравится этот план/I like this plan".
That's because when you use the verb "нравиться", it must agree with the noun(s) being liked, not the noun(s) liking it.
So, if one thing is being liked, it will be мне/тебе/ему/ей/нам/вам/им нравится
And if multiple things are being liked, it will be мне/тебе/ему/ей/нам/вам/им нравятся
Hope this clarifies it for you and happy learning! :)
I looked for a Russian version first. When I couldn't find it, I just put that link.
Comments on this page suggest that Duo has a practice of changing the verb pleases into the more common, in English, likes. They do this throughout all the language courses that translate to English.
This results in the sort of confusion that you are finding in the translation.
The Russian sentence has Мне because some people say the best translation of the example is .... This plan pleases me._
But Duo seems to think that I like this plan works better for most English speakers. Think of Duo's practice more like an opportunity to examine the difference between pleases and likes as well as the first and third person case.
Some people believe that appeals is less forceful than pleases. Others, some of whom may be quick to post, say that they don't see any difference.
Regardless, appeals is intransitive, which make it seem less direct. Pleases is transitive with the direct object being me. That makes it seem more direct.
But in the end it doesn't make any difference. Duo changed the whole structure of the sentence when translating it into English. The result is that neither pleases or appeals is accepted. The third person object is changed into the first person subject and the verb changed to like.
However much you and other students don't like the practice, clearly it appeals Duo to continue to do so. It may even please them since they do it a lot.