I have spent quite a lot of time carefully reading the arguments from both the parties. Without taking anybody's side, I would be honest to put my evaluation of the entire situation precisely below.
First of all, I must say that the essay is fairly cohesive and flows logically from A to Z. I don't agree with your statement (or your professor's) that the essay does NOT have a conclusion. It does.
Secondly, it covers the three theoreticians/philosophers fairly well, and critically includes the "voice" of the writer.
Now, I have also been thinking what went wrong that resulted in this heat and break of communication between the two of them. Reading the emails above has the answer.
If Biscuit's emails are read and critically analyzed, it is VERY clear that this person failed to really communicate to Pheelyks what HE ACTUALLY WANTED P to do with the sentences.
This irritated P and should really have because he did a pretty good job. Additionally, the tone of Biscuit in the email is not like a client but that of a master - commanding P to do this and that. This is shameful.
I will not comment on the later part in which P reacted by emailing here and there.
Now the last and final word.
To my shallow understanding, the entire problem lies (NOT WITH THE ESSAY or CONCLUSION) but with the writing level. Perhaps, Biscuit wanted to ask P to simplify the use of words, break down longer sentences into smaller ones so that it may suit his own level (because he had already decided to turn in the same paper). P didn't get him so didn't do it.
That's all from my side.