Why did ἄρρην turn to αρσενικός?
It didn’t – not directly, at least.
The pre-Greek form of the Ancient Greek word meaning ‘male, masculine, strong’ was *wŕ̥sēn. In dialects that retain /s/ after /r/, this regularly gives ἄρσην; these include Laconian, Aeolic, partly Epic, etc. In dialects where /s/ developed into /h/ after /r/ (as it did between vowels, as well as after /l/ and /n/), it yielded ἄρρην /ár̥ːɛːn/; this includes especially the most influential of all the dialects, Attic.
In Ancient Greek, both forms spawned regular derived adjectives in -ικό-: from ἄρρην came ἀρρενικός, from ἄρσην came ἀρσενικός. So far, so dialectally separate.
But as in many languages, it’s not uncommon for Greek dialects to influence each other, and for one dialect to have multiple variants of the same word sourced from different dialects. This is one such case: ἄρρην/ἀρρενικός and ἄρσην/ἀρσενικός got dialectally mixed up and were also used outside their originating dialects – and indeed, both have survived into Modern Greek, though in different ways.
In Modern Greek, the original dialect-based distinction between the two bases has been lost, and a new one has arisen, whereby the ρρ forms are used for the base adjective (άρρην) and later derivatives from it (e.g., the noun άρρενας), while the ρσ forms are used for the -ικό- adjective (αρσενικός) and any derivatives from that.
So ἄρρην did not become ἀρσενικός – rather, each used to have its own corresponding ‘partner’ (ἀρρενικός and ἄρσην, respectively) which has just been lost in Modern Greek.
Was it because αρσενικός comes from Persian word for gold and men were more important than women in the past?
Almost certainly not, no.
If we start with the Persian, it would certainly have been obvious to speakers when they formed the word *zarniya-ka- that it meant something like ‘the golden thing’ (from *zarniya- ‘golden’), and it’s quite a logical word to use for orpiment, which is indeed a lovely deep-golden colour. Indeed, the word orpiment itself comes from Latin auripigmentum ‘gold pigment’.
Later on, when Semitic speakers borrowed this word from Persian, it’s quite likely that there would still be some awareness of the origins of the word, at least amongst Semitic-speakers who were also proficient in Persian; though there would of course also be people who knew no Persian and used the word without knowing what it meant there.
But by the time the Greeks borrowed the word from whatever Semitic source is the immediate source of the Greek word, it’s highly unlikely they were aware of any connection to the Persian root. To them, it was simply a word for orpiment.
When the Greeks borrowed it, they included the definite article (as has happened quite a lot in Semitic loans, cf. alcohol, alkaline, azimuth, adobe, aubergine, etc.), so their immediate source would have been something like al-zarnīkā or al-zarnīxā.
Greek didn’t have /z/ or /x/ and generally used /s/ and /k/ (or /kʰ/) instead in loan words, so at the moment of borrowing, it would presumably have had the shape *alsarnīkā. The ending -ā would almost inevitably be reinterpreted as a feminine ending, since thematic feminines ended in -a or -ā (the latter having become -ē in some dialects). It’s almost as inevitable that *-īkā would be identified with the existing and common adjectival ending -ικᾱ́ (or -ική in dialects where ā had become ē) – only the length of the *ī was different – and the whole word perceived as a normal -ικός adjective. A masculine in -ós and a neuter in -ón would be automatically created to fill out the paradigm: *alsarnikós, *alsarnikā́ ~ *alsarnikḗ, *alsarnikón. As a noun, the name of a mineral, it was treated as neuter, *alsarnikón.
At this point in time, original Greek *ls had already become *lh > ll, and Greek didn’t really have /ls/ at all – something which would have increased the likelihood that it would get twisted into something less marked when it popped up in loan words. And *alsarnikón is of course also quite close to the existing word arsenikón (neuter form of ἀρσενικός).
That was apparently enough for arsenikón to influence *alsarnikón so much that they ended up merging entirely as ἀρσενικόν.
Remember that to the Greeks, *alsarnikón would have been an opaque word, as opaque as ‘orpiment’ is to an English speaker – the connection to a word meaning ‘gold’ in the language of origin (zar- in Persian, auri- in Latin) just isn’t there anymore. So to them, it’s just a fairly uncommon word that refers to a specific type of mineral and sounds a lot like ‘male/virile’ – enough for folk etymology to set in.
Much later, in Koine Greek, ἀρσενικόν started being used more broadly for arsenic in general, rather than only for orpiment specifically.
