1) The grammar
El placer (subject) es (linking verb) mío (predicate adjective)
It is literally "the pleasure is mine".
The sentence mjengel said would be "es mi placer". In their sentence, "It" is the subject, not "The pleasure". "Pleasure" is the predicate (albeit nominative, rather than adjective). The article is removed too, "el".
What you said would be "mi placer" (which completely removes the verb altogether). Your answer wouldn't even be a sentence.
2) "The pleasure is mine" is already an existing phrase in English.
the sentiment is the same but duo is asking you to translate "El placer es mío"
El (the) placer (pleasure) es (is) mío (mine).
The english is correct, either from the literal translation above, or the way you said it, but when the literal translation is correct, opt for that as your answer, as opposed to a similar sentiment.
I often see you saying things like this but it's misleading. The reason is not because it's a "literal translation". Some people, including myself, believe the phrase "literal translation" is an oxymoron because a translation is really an interpretation, not something which is so exact. The real reason, I believe, is that the sentence structure places the emphasis on "mio" by contrasting against the pleasure being someone else's. The other sentence structure emphasizes the word "placer" with no contrast. "Es mi placer" is a typical first sentence, whereas "El placer es mio" would be the follow-up to that.