"It is often the case in many Chinese schools of Mahayana Buddhism that an Arahant, although advanced in the path to enlightenment, has yet to reach Nirvana"
where is that stated ?
The only reference to that doctrine that I know of is from the Tibetan canon -- near the beginning of The Jewel Ornament of Liberation it says (I paraphrase), that there are five families:
- Disconnected (immodest, no compassion, no thought for others, etc.)
- Indefinite (may join one of the next three families, depending/conditioned on whether they make contact)
- Hearer (fear samsara, yearn for nirvana, little compassion)
- Solitary Realiser (like Hearer but also arrogant, keep their master's identity secret, solitary)
Hearers and Solitary Realisers engage in their respective vehicles and achieve the results of their practices, but this is not the final nirvana
If their states are not the final nirvana, then one might argue that the Buddha should not have taught these
two paths. Is there a reason the Buddha should teach such paths?
Yes. For example, suppose great merchants
from this Jambudvipa are traveling the ocean searching for jewels. After many months at sea, in some
desolate place, they become completely tired and exhausted and think, “There is no way to get the jewels
now”. When they feel discouraged and prepare to turn back, the merchant captain manifests a huge island
through his miracle power and lets all his followers rest there. After a few days, when they are fully rested and
relaxed, the captain says, “We have not achieved our goal. Now we should go farther to get our jewels.”
Eventually they are awoken by the Buddha, cultivate bodhicitta, and
practice the bodhisattva’s path for many limitless kalpas and eventually achieve enlightenment.
It says you can find this doctrine also in the Gone to
Lanka Sutra and in the White Lotus of Sublime Dharma Sutra.
These families (who haven't achieved "final nirvana") include Arhats -- towards the end it says,
The supreme worldly experiences—all the perfect powers, clairvoyance and meditative absorption, and so
forth—are achieved through devotion to the Dharmakaya. Obscuration abandonment, clairvoyance, miracle
powers, and so forth—all the qualities of Hearer Arhats—are achieved by slight realization of Dharmakaya.
Obscuration abandonment, meditative absorption, clairvoyance, and so forth—all the qualities of Solitary
Realiser Arhats—are achieved by partial realization of Dharmakaya. Obscuration abandonment, meditative
absorption, clairvoyance, and so forth—all the qualities of bodhisattvas who attained bhumis—are achieved
by greater realization of Dharmakaya.
See also Wikipedia Arhat: In Mahāyāna Buddhism.