I think you may be confusing self and individual. Or maybe, to put it more precisely, you are not confusing it but are rather using unfortunate terminology. Even computers or more primitive devices are able to tell what is part of their individual instance of their operating system and what is not. Another possible explanation could be the use of something like checksums or certificates in informatics, individual signatures confirming the integrity and origin of a part of the system. Besides, in software systems certain objects are frequently treated as consisting of one part, ‘as a whole’, whereas in reality each and every line of code and virtual ‘object’ can be traced back to a huge series of 1’s and zeroes, so that any such object may be regarded as a descriptive convention used for practical purposes. The same is true for tables and other physical macro-objects: I and, I assume, you almost never think about them as consisting of atoms but rather treat them as individual things. If this tendency to treat what we know for sure to be a descriptive convention as a really existent solid something is so deeply rooted in us, how much stronger should it be when we think about our dear self, the epicentre and constant topic of our experience!
Among other things, one can say that the idea of difference between ‘you’ and ‘me’ is often overcome in deep mystical experiences when a meditator or mysticist becomes ‘One with the World’ or, like Meister Eckhart, sees “the still desert” of the Deity, from which the world is emanating and where there is nothing and nothing aprt from nothing.
Besides, in SN 49.10 the Buddha quite unambiguously explaines why He didn’t directly teach that there is no self:
“If, Ānanda, when I was asked by the wanderer Vacchagotta, ‘Is there a self?’ I had answered, ‘There is a self,’ would this have been consistent on my part with the arising of the knowledge that ‘all phenomena are nonself’?”
“No, venerable sir.”
“And if, when I was asked by him, ‘Is there no self?’ I had answered, ‘There is no self,’ the wanderer Vacchagotta, already confused, would have fallen into even greater confusion, thinking, ‘It seems that the self I formerly had does not exist now.’”
In plain English, He didn’t teach that there is a self because it would have been plainly wrong and contradicted one of the most basic principles of His teachings, and He didn’t teach that there is no self because he wanted to avoid the same questions as the ones asked by the OP (no offence @Shaun ): ‘Wait a minute, what does it mean there is no self? I feel like I have one!’
Let’s change self (atta) to individual or person (puggala) that we will define as similar to a specific instance of an operating system working as a whole but still being nothing but a mere sequence of two characters. In that case, I will totally agree to you 100% per cent. Files that were left on your hard drives or in the cloud storage, created on your previous OS, will still be there when you install a later or more sophisticated Linux version. The analogy is not perfect because the files are also available to hackers and remotely connected devices, but then the Buddha also had knowledge about the past lives of other people and, apparently was able to read the ‘digital signature’ of these files and determine whether they were created by a previous version of His OS or a completely unrelated OS running on the other end of the world.
And then the whole idea of autonomy from other beings… Don’t get me wrong, it’s not to be interpreted as the commonplace trope of the ‘interconnectedness of everything’ or ‘we are all One’ or any other similar theory, but MN1 says more or less straightforwardly:
He perceives beings as beings. Having perceived beings as beings, he conceives beings, he conceives himself in beings, he conceives himself apart from beings, he conceives beings to be ‘mine,’ he delights in beings. Why is that? Because he has not fully understood it, I say.