https://suttacentral.net/pli-tv-bu-vb-p ... ript=latin
This is indeed an interesting one, but some clarifications :
At one time when the Buddha was staying at Sāvatthī in Anāthapiṇḍika’s Monastery,
Tena samayena buddho bhagavā sāvatthiyaṁ viharati jetavane anāthapiṇḍikassa ārāme.
1.2
the monks from the group of six were instructing lay followers to memorize the Teaching.
Tena kho pana samayena chabbaggiyā bhikkhū upāsake padaso dhammaṁ vācenti.
1.3
Those lay followers became disrespectful, undeferential, and rude toward the monks.
Upāsakā bhikkhūsu agāravā appatissā asabhāgavuttikā viharanti.
1.4
The monks of few desires complained and criticized them,
Ye te bhikkhū appicchā …pe… te ujjhāyanti khiyyanti vipācenti—
1.5
“How can the monks from the group of six instruct lay followers to memorize the Teaching?”
“kathañhi nāma chabbaggiyā bhikkhū upāsake padaso dhammaṁ vācessanti.
1.6
Upāsakā bhikkhūsu agāravā appatissā asabhāgavuttikā viharantī”ti.
1.7
After rebuking those monks in many ways, they told the Buddha. Soon afterwards he had the Sangha gathered and questioned the monks:
Atha kho te bhikkhū chabbaggiye bhikkhū anekapariyāyena vigarahitvā bhagavato etamatthaṁ ārocesuṁ …pe…
1.8
“Is it true, monks, that you do this?”
“saccaṁ kira tumhe, bhikkhave, upāsake padaso dhammaṁ vācetha;
1.9
upāsakā bhikkhūsu agāravā appatissā asabhāgavuttikā viharantī”ti?
1.10
“It’s true, Sir.”
“Saccaṁ, bhagavā”ti.
1.11
The Buddha rebuked them …
Vigarahi buddho bhagavā …pe…
1.12
“Foolish men, how can you do this?”
kathañhi nāma tumhe, moghapurisā, upāsake padaso dhammaṁ vācessatha.
1.13
Upāsakā bhikkhūsu agāravā appatissā asabhāgavuttikā viharanti.
1.14
This will affect people’s confidence …” …
Final ruling :
‘If a monk instructs a person who is not fully ordained to memorize the Teaching, he commits an offense entailing confession.’”
and also non offense Claus :
Non-offenses
2.3.1
There is no offense:
Anāpatti—
2.3.2
if they recite together;
ekato uddisāpento,
2.3.3
if they practice together;
ekato sajjhāyaṁ karonto,
2.3.4
if he prompts one who is speaking a mostly familiar text;
yebhuyyena paguṇaṁ ganthaṁ bhaṇantaṁ opāteti,
2.3.5
if he prompts one who is reciting;
osārentaṁ opāteti,
2.3.6
if he is insane;
ummattakassa,
2.3.7
if he is the first offender.
ādikammikassāti.
So you can see "reciting together" is not an offense, so being at a monastery reciting suttas with monks is not the issue here.
I believe the issue here is related to oral tradition and keeping the teachings from being diluted too much. If the monks at the time encouraged everyone and their mother to start memorizing suttas, there can be lots of divergence and confusion, a sort of "leave it to the professionals"(who were split into teams of large groups who recited the suttas together to make sure everyone had it right, a sort of self correcting mechanism) kind of mentality. If you notice when a monastic is there with the lay person, its ok.
This could also be seen as something that interrupts society, if laity spent their time memorizing instead of working the farm with their family etc etc, becoming a monastic allowed for the vessel of the teachings to be kept more organized and pure.
You also have to keep in mind that at the time of the Buddha, only the Brahmins memorized and recited the vedas, it was a high caste very important thing, if the Buddhists encouraged laity to start memorizing and reciting, it could of caused social strife, especially if low caste people are doing it.