Translation:In spite of his opinion, she is learning many languages.
Pigs could fly. Centuries of human experience show that in fact they don't. Learning more than one language could hinder your progress, but centuries of having classical languages as part of a well-rounded education suggests that it doesn't.
Anyway, I don't see where it says she is learning all those languages at once. Neither do I read anything about setting aside too little time for each individual language. If someone has the time and inclination to have their normal week consist of Englishday, Frenchday, Norwegianday, Spanishday, Latinday, Greekday, and Sunday, I doubt it will really decrease their language pace below that of two hours a week of disinterested language. (I would allow for the claim that the distribution throughout the week could be improved upon, though.)
Well, as for masukomi's question, I think the key part you're missing is the "da." Saying "multe da lingvoj" is just a phrasal way of saying "a lot of languages." If you don't want to use "da," then "multajn lingvojn" can also work here. And as for you, it's probably not a good idea to go in looking for "fluency" so quickly! It'll only serve to frustrate you, as it apparently has already.
A reasonable fluency in a language tends to require some 600 hours of study. The problem doesn't seem to be the amount of grammar. Rather, the grammar work is apparently dwarfed by the sheer volume of vocabulary work. Sure, Esperanto might have an easier grammar, but that doesn't magically make you fluent.
These 600 hours, if take in three months, will mean 200 hours each month -> more than 6 hours PER DAY of studying. There are very few humans that sit staring at the wall for 7 hours each day, so to get that speed, you'll have have to freeze enough other activities to make at least that amount of time available.
I don't know who promised you fluency in three months, but I expect it meant that you would grasp its entire grammar in three months. You still would have nothing to say after that time, but at least you would know how to say that.