about the reason for "ἀπεκρίνω" the aorist mp of "ἀποκρίν"ω

So, I am reading Plato’s Protagoras, and at one point this verb appears (To discern, set apart) I though at first that it was in indicative singular first person, but not making much sense in context, I contrasted with the perseus tool (http://www.perseus.tufts.edu/hopper/morph?l=a)pekri%2Fnw&la=greek&can=a)pekri%2Fnw0&prior=a)\n&d=Perseus:text:1999.01.0177:text=Prot.:section=311c&i=1), and to my surprise it was in aorist, mp, 2nd singular.
Now I understand that the ‘-ε-’ in ‘ἀπε-’ is from the augment of the sigmatic aorist, and that the “-ω” at the end is the result of a contraction between alpha and omicron as the result of the disappearence of sigma after the ‘-σα-’ (from the aorist sigmatic) from the second declension of the middle person (‘-σο’). However, per my knowledge of the rules, the result should be ‘ἀπεκρίσω’ as it is the nu wich disappears and not the sigma when one is besides the other, but it seems that in this case the nu wins, ¿how is that possible?¿what am I missing?

The aorist of κρίνω, from which ἀποκρίνω (< ἀπό + κρίνω), is ἔκρινα. It’s not a sigmatic aorist. The middle aorist is ἐκρινάμην and the second person singular is ἐκρίνω.

λύω → ἐλυσάμην
λύεις → ἐλύσα[σ]ο = ἐλύσω

However, for verb-endings beginning with σ, verb-stems that end in liquids (λ,μ,ν,ρ) lose σ and lengthen the preceding vowel. See Smyth 544.

κρίνω → ἐκρινάμην
κρίνεις → ἐκρίν[σ]α[σ]ο → ἐκρίνω

You may wish to take a look at Smyth 402 for the conjugation of the consonant verb φαίνω for an example.