Q:

Why don't minimal pairs like "быть" and "бить" prove that /ɨ/ and /i/ are separate phonemes in Russian?

In analyses of Russian, there's a dispute about whether the vowels /ɨ/ and /i/ (typically represented in the orthography as "ы" and "и", respectively) are separate phonemes, or if [ɨ] is an allophone of /i/.
Quoting Wikipedia,:

The five-vowel analysis, taken up by the Moscow school, rests on the complementary distribution of [ɨ] and [i], with the former occurring after hard (non-palatalized) consonants and [i] elsewhere.
The six-vowel view, held by the Saint-Petersburg (Leningrad) phonology school, points to several phenomena to make its case:

Native Russian speakers' ability to articulate [ɨ] in isolation (for example, in the names of respective letters, ⟨и⟩ and ⟨ы⟩),
Rare instances of word-initial [ɨ] (including the minimal pair икать 'to produce the sound и' and ыкать 'to produce the sound ы'), as well as borrowed names and toponyms, like Ыб About this sound [ɨp], the name of a river and several villages in the Komi Republic.
Morphological alternations like готов [ɡɐˈtof] ('ready' predicate, m.) and готовить sound [ɡɐˈtovʲɪtʲ] ('to get ready' trans.) between palatalized and non-palatalized consonants.

The most popular view among linguists (and that taken up in this article) is that of the Moscow school, though Russian pedagogy has typically taught that there are six vowels (the term phoneme is not used)

The first and second arguments for the Saint-Petersburg school don't seem particularly compelling to me, since they could easily be artifacts of Russian pedagogy that would be expected if the orthography distinguishes sounds that are actually allophones. I'm not sure I fully understand the third argument.
But absent from these arguments is any mention of minimal pairs like быть (/bɨtʲ/ "to be") and бить (/bitʲ/ "to beat") or мыло (/mɨlə/ "soap") and мило (/milə/ "cute"). Is there something I'm missing? Why wouldn't these examples indicate that /ɨ/ and /i/ are separate phonemes?

A:

This is because they are not minimal pairs. They differ in a consonant. The "бить" has soft б while "быть" has hard б.

