“It is necessary that saying and thinking actually are. For being exists, and
nothing does not exist. I command you to ponder these things. For I shut you out from this first inquiry; moreover since it is from this, on which mortals who know nothing wander, being two headed. For helplessness keeps straight the wandering mind in their breasts: and the dumb and likewise the blind are carried around, astounded and confused people, for whom being and non-being are considered the same thing and not the same thing, and their (i.e. of the dumb and blind) path turns back” (DK Frag. 6 :1-9).”

Χρὴ τὸ λέγειν τε νοεῖν τ΄ ἐὸν ἔμμεναι· ἔστι γὰρ εἶναι,
μηδὲν δ΄ οὐκ ἔστιν· τά σ΄ ἐγὼ φράζεσθαι ἄνωγα.
Πρώτης γάρ σ΄  φ΄ ὁδοῦ ταύτης διζήσιος <εἴργω>,
αὐτὰρ ἔπειτ΄  πὸ τῆς, ἣν δὴ βροτοὶ εἰδότες οὐδέν
πλάττονται, δίκρανοι·  μηχανίη γὰρ ἐν αὐτῶν
στήθεσιν ἰθύνει πλακτὸν νόον· οἱ δὲ φοροῦνται.
κωφοὶ ὁμῶς τυφλοί τε, τεθηπότες, ἄκριτα φῦλα,
οἷς τὸ πέλειν τε καὶ οὐκ εἶναι ταὐτὸν νενόμισται
κοὐ ταὐτόν, πάντων δὲ παλίντροπός ἐστι κέλευθος.

With the consideration that Parmenides wrote in hexameters, and that such works were often recited in public, and that Parmenides himself is portrayed by Plato as being present at such a recital of one of his own students [1], I approach this particular fragment differently than if it were merely a philosophical treatise, void of cultural context.
Saying, by existing, is a thing.  The “being-ness” of words is casually assumed by their very use, yet their use qua existence is unreflectively maintained, absent the awareness which appreciates even the possibility of the existence of words.  This “being-ness” of words is re-iterated for the uncognizant by the very fact that Parmenides is speaking words at them, at the audience.  We are incapable of thinking of non-existence.  For any thinking involves the thinking of a thought as thing, a thing which must exist to be a thing.  If it is thought, it is not a nothing, but a something, even if that something is merely a thought (i.e. a unicorn).  We can not think of non-being, for if we could, it would be a being we were thinking of, not non-being.

Therefore all is being.

[1] ἀναγιγνώσκειν οὖν αὐτοῖς τὸν Ζήνωνα αὐτόν (Parmenides 127c)
“Zeno himself was reading to them…”  A few lines later Parmenides comes in to hear the end of the reading.