In coin flipping protocols, why aborting is allowed, and why the non-aborting party flips a coin at the end?
1.
You usually allow parties to abort at will at any stage of the protocol since a malicious adversary can always do that in a real protocol execution, and therefore this is not something we can enforce. 
A bit more formally, the best we can simulate (for a tutorial on simulation-based proofs see this) is an adversary that can abort, since that's unavoidable anyway.

2.
I didn't read the details of the paper but I assume that in the description, Bob still throws a coin if Alice aborts. 
This is done precisely to break the bias imposed by Alice with the abort.
This works because Bob is honest (since Alice is malicious as she aborted) so the output, that is, the coin tossed by Bob, will have a uniform distribution.