I think AN 10.29 Paṭhamakosalasutta already shown the answer you need. At the end of the sutta, the Buddha explicitly said his assertation and statement, I have highlighted in bold for you:
There are some ascetics and brahmins who advocate ultimate extinguishment in this very life. This is the best of those who advocate extinguishment in this very life, that is, liberation by not grasping after truly understanding the origin, ending, gratification, drawback, and escape of the six fields of contact. Though I state and assert this, certain ascetics and brahmins misrepresent me with the false, hollow, lying, untruthful claim: ‘The ascetic Gotama doesn’t advocate the complete understanding of sensual pleasures, forms, or feelings.’ But I do advocate the complete understanding of sensual pleasures, forms, and feelings. And I advocate complete extinguishment by not grasping in this very life, wishless, extinguished, and cooled.”
Also in Paṭhamakosalasutta AN 10.29, if you look more carefully, the reason that he didn’t encourage “convictions of outsiders” is because:
Some sentient beings have such a view. But even the sentient beings who have views like this decay and perish.
In other words: “decay and perish” just like among the list of other kinds of sentient beings mentioned above at the upper part of the sutta.
In other words: such view is also wrong view that is not within the Noble Eightfold Path (which includes Right View instead).
After he rejects such “convictions of outsiders” which links to “you can expect that they will be repulsed by continued existence, and they will not be repulsed by the cessation of continued existence”, he moved on to reject “advocates of the ultimate purity of the spirit” which links to “dimension of neither perception nor non-perception”. He encouraged instead “ultimate extinguishment” (which is another word for Nibbāna).
So, “repulsed by continued existence and not repulsed by the cessation of continued existence” is NOT the same as “ultimate extinguishment”. However, when compare to “not repulsed by continued existence and not repulsed by the cessation of continued existence”, the other one is still closer to “ultimate extinguishment”. That’s why it’s still considered as “the best of the convictions of outsiders”.
The critical part is: Why it is wrong view?
My answer (without invoking “atta”) is: It is wrong view because this view got clinged on without truly understanding and realizing “ultimate extinguishment”. Further clarification: When someone truly understands and realizes “ultimate extinguishment”, it is not correct to say “exist” (“more of existence” is not attractive), it is not correct either to say “not exist” (“no more of existence” is not attractive either). And why it is not correct to say “exist” or “not exist” or “exist and not-exist” or “neither exist nor not-exist”? Further clarification: “ultimate extinguishment” is outside of phassa (contact) while such “exist” and “not exist” can only be defined through phassa.
I think you are aware of the quite famous Yamakasutta SN 22.85 too.
The following is an illustration: Someone heard of the mountain Everest. He got a view that this mountain Everest is the highest point on the planet, a very cold place, a very famous place. He clings on this view so he will never be at ease and inevitably gets into debate when someone else says something like “No, you are wrong, mistaken. This Mauna Kea is truly the highest mountain”. As Everest is a conditioned dhamma, there will inevitably be a time that his clinging view will be challenged. In other words, he can’t be at ease. It’s worth noting here, the “experience” that the person got such as climbing the Everest himself will actually makes the clinging even stronger as “I myself-nobody-else experienced my-climbing-of-Everest”.
So, how can he be at ease with this Everest matter? By realizing that not only Everest but his view about Everest and also his “experience” with Everest are all conditioned dhamma. Therefore, he stops the clinging with Everest, the clinging with his view about Everest, the clinging with his own “experience” with Everest.
And how can he be at ease with anything? By realizing the “ultimate extinguishment of all conditioned dhamma” through “not grasping after truly understanding the origin, ending, gratification, drawback, and escape of the six fields of contact”
Hope that this explanation can be of useful.
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