This can appear as a "type what you hear" exercise as well. It definitely seems to me that "βήτα" should be accepted when the correct answer is "β."
It's a good question. Here's a phonological answer. The sound [b] is a voiced bilabial plosive, while [v] is a voiced interdental fricative. Interdentality and bilability are quite similar, so as two of the three main articulatory features are the same or close to the same (i.e., the only major difference between the phones is the manner of articulation), it's not surprising that they should be treated similarly.
Note, however, that Greek does indeed have completely separate sounds for both [v] and [b]. The former is of course represented by the letter β; the latter is written μπ. That is, "μπράβο" is pronounced [bɾavo]. From a linguistic perspective, this also makes sense: the phone [m] is a voiced bilabial nasal, which is essentially the quintessence of voicing; when an unvoiced consonant follows it, the resulting sound is the same as the sound of the corresponding voiced consonant (albeit with a high voice-onset time). As [p] is the unvoiced version of [b] (an unvoiced bilabial plosive), the result follows.
What we are showing here is the correct Modern Greek pronunciation of the Greek letter Ββ. See here for a fuller view of the alphabet: https://forum.duolingo.com/comment/22424028
Knowing the name of the letter will not assist you in using the langauge it's the way it's pronounced that you'll need.
And for other resources see here:https://forum.duolingo.com/topic/936
The link I gave you above will bring you to a lot of information about this course.
Please read the Tips ¬es for this Skill then move beyond it and on to more interesting and better-constructed skills.
I think you'll find Basic 1 much more rewarding. Please read the Tips & notes before you begin and us the Drop-down hints to find the precise word for the translations.