I am a fourth year university student and a 1 year internship is required before I can work professionally in my field. I recently accepted an offer to join an internship on the conditions that I complete the GRE with a suitable score and apply to their graduate school as soon as possible. The GRE and the graduate school applications needed to be completed in under two weeks.
From almost the start I have had difficulty in communicating with the internship director. I began email communications with him which was fine. However, I had to leave for the weekend and told him to call me and leave a message if there was anything important I needed to know since I would be unable to check my email or respond during the (professional) event I was going to. The message he ended up leaving was fine, but the number he left was incomprehensible. Furthermore, my phone was off so it wouldn't disturb me or others during this event so I didn't get his caller ID.
As soon as I got back I replied to his message via email and explained the situation, asking for his number as well as some other information that I needed from him to finish the graduate school application and send him the fees he wanted. I received a response of "Glad to help." and was told he was waiting on my GRE score. I was put off by this at first since he didn't actually answer anything, but I instead took it to mean he wanted my GRE score first before he would reply. I can understand that. However, I needed the information to apply to his graduate school in the next few days but could not get a response out of him despite my emails. I ended up guessing on part of my application and hoping that the information was correct.
All these emails were through my university email account. However, this would be closing soon due to me graduating so I told him after the "Glad to help." email to send any future emails to my alternate email account.
I took the GRE the next week and sent my scores to the University. That same day there was a personal tragedy in my family so I did not check my email for four days. After those four days I checked my email to see one from him saying that, due to my poor communication in response to his repeated emails, he has given my slot to someone else.
I have checked and triple checked both my university and alternate email but have received no emails from him after the "Glad to help." email. He did not call, either, despite knowing that I could get his messages since I referenced it in previous emails. I responded to this email explaining that I haven't gotten any of these emails and that the "Glad to help." one was the last I received. He has since told me he may reconsider if I keep good communications and has stressed that it's rude to leave his program after accepting his offer, specifying that students have been known to use his program for "ulterior motives".
I understand that not following through with my acceptance is rude, but I have done everything requested, including sending fees, and have now been labeled as a "poor communicator" despite my efforts to maintain contact. To me, this is a huge red flag and I don't know if I should accept his reconsideration, IF he even offers it. Furthermore, I don't want to (re)accept his offer and take away the slot from someone else.
My question is whether or not this is as big of a red flag as I see it? If so, should I accept his offer if he reconsiders?
EDIT: Thank you all for the helpful suggestions. For some more context, a master's degree is optional with this internship but graduate school admission and the GRE are required regardless. I was informed of this internship on very short notice (a few days before the deadline) from a faculty member at my university. I accepted the offer so as to ensure getting an internship with the written and explicit understanding that the GRE would be completed a week after the graduate school deadline since the university and the director accept late GRE scores.