I had to read this a few times...but the takeaway is, you were being taught MSA by a Yemenite? My impression is that you've been learning Arabic for some time now. I guess it's mostly been written, outside of teaching sessions? I was recently reading up more on the MSA/colloquial issue and was particularly curious as to why so many non-natives tend to study MSA primarily or exclusively, when it's not spoken anywhere. Does that make any of the spoken varieties understandable to you? Do you use Arabic for anything outside of the written word currently?
Yes, my teacher was Yemeni and yes, it was mostly written and no, I'm not using it for anything except writing right now.
On the MSA/dialect front, MSA made it possible for me to communicate with Sarah, Ashraf and Niaz (Yemeni - Aden and Ibb areas, respectively) and with Aida and Anis (Tunisia). If I really learned a dialect, I would only be able to communicate with people speaking the same dialect (which might not even cover a country, see Yemen).
MSA is what I guess Arabic natives default to when asked to "teach me Arabic" for presumably that reason. I believe they also default to speaking MSA to foreigners (be it Yemenis in Tunisia or Caucasians generally). MSA is also taught in Turkey at least to some degree (my Kurdish friend would laugh and nod and remind me it's not Turkish, but she understood me and replied in kind).
I've never had any chance to listen to the spoken varieties. Yemen has a LOT of dialects and it's difficult to find any material specifically from that country. I might have better luck trying to find a sample of Tunisian Arabic, but then, I need to practice my listening on Maha first (as it was nonexistent before I got the headphones - joys of being hearing-impaired)