Why will Artemis II not orbit the Moon?

Question

The Artemis II mission will loiter in an elliptical, high-Earth orbit before the Orion uses its own propulsion to complete the trans lunar injection (tli), thus using the fuel it might’ve otherwise used to insert itself into lunar orbit. A traditional mission would use the launch vehicles upper stage to complete TLI. Why is this not being done for Artemis II?

Answer 1

Artemis II will have Orion conduct proximity operations testing in preparation for docking with HLS on Artemis III. The ICPS (Interim Cryogenic Upper Stage - SLS block I's final stage) will be used as the object to conduct this test with, therefore Orion needs to detach from it. Since the ICPS has a (relatively) limited loiter time (Quora warning. Also re: A1), and must also perform its own disposal burn after separating from Orion, the prox ops testing is to be performed at the start of the checkouts. This means it will be performed before the orion propulsion checkouts. Because Orion's main propulsion system is needed for an abort from lunar orbit - and even to reach lunar orbit - the prox ops testing will occur in earth orbit. This way, if there are problems with the main propulsion system, Orion can use its secondary propulsion system to return to Earth.

Because of these constraints, Orion cannot be injected into TLI by ICPS, and will need to finish the manoeuvre itself, which, as you noted, does not leave it with enough fuel to insert into Lunar orbit.

Here is an archived NASA article that discusses more details of the mission's design.