No actually you did not and ignored the lexical definitions
Sorry the word draw does not mean to chose
εἵλκυσεν. Hebrew equivalent: משׁך (1).
Verb Usage
1.
to draw (from container)† — to bring, take, or pull out of a container or from under a cover. See also σπάω.
Jn 18:10 Σίμων οὖν Πέτρος ἔχων μάχαιραν
εἵλκυσεν αὐτὴν
Jn 21:6 οὐκέτι αὐτὸ
ἑλκύσαι
Jn 21:11 καὶ
εἵλκυσεν τὸ δίκτυον εἰς τὴν γῆν μεστὸν ἰχθύων μεγάλων
2.
to seize away ⇔ haul† — to lead someone away by force against their will; conceived of as drawing a heavy object out of something with great effort. See also ἕλκω.
Ac 16:19
εἵλκυσαν εἰς τὴν ἀγορὰν ἐπὶ τοὺς ἄρχοντας,
3.
to attract powerfully ⇔ haul† — to attract powerfully, conceived of as drawing a heavy object out of something with great effort.
Jn 6:44 ὁ πατὴρ ὁ πέμψας με
ἑλκύσῃ αὐτόν,
Jn 12:32 κἀγὼ ἐὰν ὑψωθῶ ἐκ τῆς γῆς, πάντας
ἑλκύσω πρὸς ἐμαυτόν.
Rick Brannan, ed.,
Lexham Research Lexicon of the Greek New Testament (Lexham Research Lexicons; Bellingham, WA: Lexham Press, 2020).
ἑλκύω s. ἕλκω fut. and aor.
ἕλκω impf. εἷλκον; fut. ἑλκύσω; 1 aor. εἵλκυσα; for the forms w.-υ-s. Mlt.-H. 236; Bl-D. §101 p. 45 (Hom.+; inscr., pap., LXX, Joseph.) drag, draw.
1. trans.—a. lit. τὶ someth. a sword (Soph., Ant. 1233; Libanius, Or. 13 p. 73, 5 F. ξίφος) J 18:10; haul a net 21:6, 11; τινά (Diod. S. 34+35 fgm. 2, 14 τινὰ εὒς; Achilles Tat. 7, 15, 4 εἷλκόν με εἰς τὸ δεσμωτήριον; Jos., Bell. 1, 591 τινὰ εἰς.—Also Clearchus, fgm. 73; Diod. S. 14, 5, 3 ἕ. τινὰ ἐπὶ τὸν θάνατον) ἔξω τ. ἱεροῦ drag someone out of the temple Ac 21:30; εἰς τ. ἀγορὰν ἐπὶ τ. ἄρχοντας 16:19; εἰς κριτήρια hale into court Js 2:6 (Herodas 5, 59 ἕ. τινὰ εἰς τὰς ἀνάγκας=to punishment). οἱ ἕλκοντες ἡμᾶς LJ 2:3 is expanded by Dssm. w. εἰς τὰ κριτήρια; differently by others. Actually nothing need be supplied, since ἕ. τινά means pull or tug someone back and forth, mistreat someone (Libanius, Or. 58 p. 183, 20 F. ἕλκων κάπηλον; cf. Jos., Bell. 1, 338: εἷλκεν τοὺς ἔνδοθεν). Of stones ἐκ τοῦ βυθοῦ ἑλκομένους which were dragged out of the deep Hv 3, 2, 6; 3, 5, 2.
b. fig. of the pull on man’s inner life (Pla., Phaedr. 238A; Aelian, Nat. An. 4, 13; Porphyr., Marc. 16 μόνη ἡ ἀρετὴ τ. ψυχὴν ἄνω ἕλκει καὶ πρὸς τὸ συγγενές; Jer 38:3; SSol 1:4; 4 Macc 14:13; 15:11; Jos., Ant. 15, 27)draw, attract J 6:44. ἕλκ. πρός with acc. (Hierocles 25 p. 477 it is said of God ἐλκύσαι πρὸς τὴν ἀλήθειαν τοὺς ἀνθρώπους): πρὸς ἐμαυτόν 12:32.
William Arndt et al., A Greek-English Lexicon of the New Testament and Other Early Christian Literature : A Translation and Adaption of the Fourth Revised and Augmented Edition of Walter Bauer’s Griechisch-Deutsches Worterbuch Zu Den Schrift En Des Neuen Testaments Und Der Ubrigen Urchristlichen Literatur (Chicago: University of Chicago Press, 1979), 251.