"I dream of being a professor." This adjustment has been made in other Duolingo language courses. It should be made here too, now.
indicative # subjunctive
eu sunt # să fiu
tu ești # să fii
el/ea este # să fie
noi suntem # să fim
voi sunteți # să fiți
ei/ele sunt # să fie
I don't know... You can form the Romanian sentence "Visul meu este să fiu profesor" which is a direct translation of your version. As long as there's a direct translation in the target language (English) of the source sentence, and the source language (Romanian) has a direct translation of your alternative, you should avoid it, at least for a beginners' course.
I hope the last sentence is readable; my point was clear to me but it came out a mess...
WilliamCorujo's point might have been that the English translation "I dream to be a professor" is not idiomatic at all. We would rather say what he offered, or "I dream of being a professor." We dream "of," not "to."