There are many instances where the phrases of possibility and ability don't mean in the absolute sense, even in the modern English, like "I cannot commit adultery, I is impossible that I may betray my wife". The sense is not of physical possibility but that I would not, implying certainty, imperative and intention. "Would" also indicates certainty or uncertainty. The difference between the nuances of shall and will has also a similar effect where "will" shows certainty.
Since the ancient languages did not contain verbs and adverbs of justification and disclaimer, the modern reader who is used to hear the adverbs like almost in every general statement tend to misunderstand them. Thus we have absolutely no general statements in the postmodern language of the modern times. Few examples in English:
"His ideas sound impossible."
(sound, seem, be: is/am/are, appear, look, prove)
"The bad weather made it impossible to play baseball."
"I find it impossible to stay mad at him."
"He is impossible to work with."
(be: is/am/are, be + becoming, remains)
"It is absolutely impossible to finish the project today."
(absolutely, completely, totally, utterly, humanly, downright)
"It is almost impossible to reach him during the day."
(almost, nearly, practically, virtually, simply, pretty)
"Her handwriting is literally impossible to read."
"It is physically impossible to achieve that goal."
(physically, technically, scientifically, mathematically, logically)
"You are just impossible to live with."
(just, simply, absolutely, completely, quite, totally)
Reading the verses in context helps to understand the sense. The same figurative sense of certainty applies to other verses about not being capable of sinning, or the impossibility of apostates to repent back to God.
1 John 3:9: “Whoever is born of God does not commit sin, because his seed remains in him; and he cannot sin (ού δύναται not able to) , because he is born of God.” (NHEB)
Luke 17:1: “He said to the disciples, “It is impossible that no occasions of stumbling should come, but woe to him through whom they come.”
Matthew 7:18: “A good tree cannot produce evil fruit, neither can a corrupt tree produce good fruit.”
Hebrews 6:4: ἀδύνατον (impossible): “For it is impossible in the case of those who have once been enlightened, tasted the heavenly gift, become partakers of the Holy Spirit,” NET
BDAG3 on αδύνατος
ⓑ subst. οἱ ἀδύνατοι (Hyperid. 2, 10 contrasted w. δυνάμενοι εἰπεῖν, those who cannot speak; TestJob 45:2 [w. πτωχοί in a gener. sense]) of those weak in faith (opp. οἱ δυνατοί) Ro 15:1.—τὰ ἀδύνατα what is powerless Dg 9:6b.—τὸ ἀδύνατον inability εἰς τὸ τυχεῖν 6a; τὸ καθʼ ἑαυτοὺς ἀδύνατον εἰσελθεῖν our own inability to enter 9:1. Cp. δύναμαι w. neg.
② incapable of happening or being done, impossible (Pind., Hdt. et al.; LXX, Philo, Joseph.; Ar. 5, 2; Just.; Tat. 20, 2; Ath.).
ⓐ adj. ἀ. w. and without ἐστίν (B-D-F §127, 2) it is impossible Hm 11:19ab; παρὰ ἀνθρώποις τοῦτο ἀ. ἐστιν Mt 19:26; Mk 10:27 (cp. Philo, Spec. Leg. 1, 282; Jos., Ant. 10, 196; PCairZen 31, 8 [III b.c.]; dedicatory ins fr. Phrygia in Steinleitner 59, no. 31, 4f: Μητρὶ Λητῷ ὅτι ἐξ ἀδυνάτων δυνατὰ ποιεῖ.—Ps.-Lucian, Halc. 3 ἀδύνατος and δυνατός of that which God cannot and can do); οὐδὲν ἀ. παρὰ τῷ θεῷ 1 Cl 27:2 (cp. Pind., P. 10, 48–50); cp. Lk 18:27. W. inf. foll. and acc. w. the inf. (Wsd 16:15; 2 Macc 4:6; Jos., Ant. 5, 109; Ar., Just., Ath.) Hb 6:4, 18; 10:4; 11:6; Hs 9, 26, 6; MPol 6:1. οὐκ ἔστιν ἀ. ὑπὲρ ὀνόματος θεοῦ (sc. τοῦτο ποιεῖν) IPhld 10:2.
to possess capability (whether because of personal or external factors) for experiencing or doing someth., can, am able, be capable.
ⓐ w. inf. foll.
α. pres. inf. (Poyaenus 8, 10, 3 φέρειν δύν.) οὐδεὶς δύναται δυσὶ κυρίοις δουλεύειν Mt 6:24; Lk 16:13.—Mt 9:15; 19:12; Mk 2:7, 19 al. καθὼς ἠδύναντο ἀκούειν Mk 4:33 (w. ref. to level of understanding; cp. Epict. 2, 24, 11). Expressed with strong emotion in rejection of what is heard τίς δύναται αὐτοῦ ἀκούειν Who can listen to such talk! (REB) J 6:60. οὐ δ. ἀναστὰς δοῦναί σοι I’m in no position to get up and grant your request Lk 11:7. οὐ δυνάμεθα … μὴ λαλεῖν we cannot remain silent τὶ about someth. Ac 4:20. In questions πῶς δύνασθε ἀγαθὰ λαλεῖν; how can you say good things? Mt 12:34. πῶς δύναται σατανᾶς σατανᾶν ἐκβάλλειν; how can Satan drive out Satan? Mk 3:23; cp. J 6:52; Lk 6:42.
β. aor. inf. (IAndrosIsis, Kyme 4; Just. A I, 2, 4 ἀποκτείναι μὲν δύνασθε, βλάψαι δʼ οὔ; Ath. 15, 1 διακρῖναι οὐ δυνάμενοι) δύνασθαι … εἰσελθεῖν Mk 1:45.—2:4; 5:3; Lk 8:19; 13:11; 14:20 and oft. The impf. ἐδύνατο τοῦτο πραθῆναι this could have been sold Mt 26:9 (B-D-F §358, 1; cp. Wsd 11:19f).
γ. likew. the impf. w. pf. inf. ἀπολελύσθαι ἐδύνατο he could have been set free Ac 26:32.
ⓑ abs., whereby the inf. can easily be supplied (cp. Eur., Or. 889; Thu. 4, 105, 1; X., An. 4, 5, 11 al.; Sir 43:30; Bar 1:6; 1 Macc 6:3; 9:9, 60; 4 Macc 14:17b; ParJer 4:6 cod. C ἠδυνήθητε ἐπʼ αὐτῇ [s. ἰσχύω]; Just., A II, 15, 2 ἵνα εἰ δύναιντο μεταθῶνται ‘in the hope that they might possibly be converted’) Mt 16:3 (sc. διακρίνειν); 20:22b; Mk 10:39 (sc. πιεῖν); 6:19 (sc. ἀποκτεῖναι); cp. Lk 9:40; 16:26; 19:3; Ac 27:39; Ro 8:7. καίπερ δυνάμενος although he was able to do so 1 Cl 16:2. οὔπω γὰρ ἐδύνασθε (sc. χρῆσθαι τῷ βρώματι) you were not yet strong enough (=‘you were not yet up to it’) 1 Cor 3:2. ὑπὲρ ὸ̔ δύνασθε (sc. ἐνεγκεῖν) beyond your capability 10:13.