Here are my 2 cents
First of all I have to say that in the most important part of the ATC communication recording, the pilot communication has clearly been cut. Deliberately or not, I don't know. This phrase ''Yes, TORA is two two, actually, sorry, TORA is ah One Two Seven Three Meters, I assume that is not enough.'' is said by the controller. It's the same voice, same accent, that's clear as day. There appears to be some confusion with this part.
The most plausible theory I read so far which is what I think happened in that day is this one and I will quote user V__2:
''I suspect having lined up at the wrong intersection, in haste the crew typed and searched for D5 into the EFB which spat out some numbers, but it went un-noticed that D5 was for 12R not 30L.''
What I suspect happened: The pilots turned at D5 by mistake. They suddenly realised they had lined up at the wrong intersection and in a hurry to leave the active runway instead of back tracking they immediately started to recalculate new TORA from D5. In a hurry they mistakenly selected D5 for rwy 12R where they got 2266 meters of available runway which would be more than sufficient in this case. There is no Embraer instructor captain who would consciously elect to start the take off run of a fully loaded E195 with 1200 meters of runway available. Unless they were looking for a suicide attempt.
Psychological factors come into play:
Confirmation bias: Even though we know for a fact that they were given the exact correct TORA from the ATC, my suspect is that in their mind they were convinced they had 2226 meters of TORA. They were suddenly overwhelmed trying to recalculate everything on an active runway and the ATC information which they were given didn't properly kick in. The initial confusion of the TORA from the ATC: ''Yes, TORA is two two, actually, sorry, TORA is ah One Two Seven Three Meters'' might have been an additional factor.
Tunnel vision: We know that at least the captain was based in BEG and should be very familiar with the airport. This leads to the idea that just based on the vicinity of the aircraft with the terminal building he would easily tell that this is not a correct position to depart. However in a hurry (and maybe a little embarrasment for a instructor captain to turn at the wrong intersection) and busy looking at the EFB, it is very possible that he might have missed this important hint.
There are also unconfirmed rumours that the FO was on a line check flight. CRM issues is very possible plus unfamiliar pilot with LYBE. Combination of embarrassed instructor captain trying to get out of the situation as quick as possible + unexperienced and nervous FO.
Anyone feel free to correct me whether this chain of events is possible or not, thank you.