Once you get a T4 curtailment letter you have two options: (1) find another school that will take you in and apply for a new T4; or (2) leave the UK. Thus once the curtailment date arrives you must either have a new visa or be gone (or become illegal).
My question is why would then the curtailment letter set out a
There needs to be an absolute date because you cannot stay forever; they give you some time to close down your personal affairs (or find a new school). The rules about setting the date and how much time they give you were set (implicitly) by Parliament and there is no latitude for discretion.
why it would say leave to enter?
Admittedly, it sounds like an oxymoron, but 'leave' in this sense means 'permission'. In context, the whole phrase 'leave to enter' roughly means 'permission to enter or remain'. They use that terminology because it needs to be consistent with the terminology in the Immigration Act 1971.
Can someone help me understand why I can't enter the UK to finish up
or apply for an extension?
Your time to apply for an extension from within the UK finished on your curtailment date. And you cannot enter the UK to finish up because you need a T4 visa to do that and since you are outside of the UK it means your T4 needs to be issued in the form of an entry clearance, and Paragraph 28 says that an entry clearance can only be obtained from outside of the UK.
I understand that these things can seem like a cruel tautology, so it's best accepted as a part of WHAT IS. None of the legal theory and variegated history of the T4 regime will progress your situation until you get a new T4.
You did not give the reason for your curtailment, but in most cases the school told UKVI that you were not attending classes or failing your classes or otherwise not performing like a student and they were done with you. They wrote you off and they were legally required to tell UKVI about it. It means UKVI was in reactive mode and was not the instigator.
One further note... I took a legal course devoted to T4 visas and the instructor advised us that if things reached the curtailment stage the person had generally burned their bridges with the school because the person was deemed an unacceptable risk. So you should check with the Authorising Officer at your school to see if 'finishing up' is actually in the cards for you.