The grammatical structure found in Hebrews 6:6 appears to be the impersonal use of the predicate adjective in the neuter case (nominative singular form). That is, “it is impossible..." The subject is an infinitive, general thought (Smyth §1047), or statement of general truth (Smyth §1048). In other words, this grammatical structure is a blanket statement of propositional truth.
On the other hand, the grammatical structure in 1 Jn 3:9 appears with similar nuance. For example, the exact same sequential syntactical structure occurs 33 times in the NA28 Greek New Testament with the verb δύναμαι. In this regard, please click on the image below for better viewing.
Thus the same exact sequential structure suggests the same blanket statement idea. In the strict grammatical sense, there is no hair-splitting between “not able to” versus “cannot” -- that is, the idea is absolute. The context in First John however must refer to something else, because the text indicates that all believers are sinners. The word for “have” in the following verse (ἔχω) is in the present active indicative, which suggest action in present time.
1 John 1:8 (NASB)
8 If we say that we have no sin, we are deceiving ourselves and the truth is not in us.
The idea of sinless existence does not appear to be in view then. That is, on the one hand, the believer remains with sin (1 John 1:8) but on the other hand, the believer is “not capable” of sinning (1 Jn 3:9). Henry Alford (1976) has addressed this apparent conundrum as follows:
. . . the plain words of the Apostle must be held fast, and explained by the analogy of his way of speaking throughout the Epistle of the ideal reality of the life of God and the life of sin as absolutely excluding one another. This all the best and deepest Commentators have felt: so Augustine and Bede, “in quantum in ipso manet, in tantum non peccat.” [In so far as man is found in one, to that extent he sins not.] The two are incompatible: and in so far as a man is found in the one, he is thereby separated from the other. In the child of God is the hatred of sin; in the child of the devil, the love of it; and every act done in virtue of either state or as belonging to either, is done purely on one side or purely on the other. If the child of God falls into sin, it is an act against nature, deadly to life, hardly endured, and bringing bitter repentance: it is as the taking of a poison, which if it be not corrected by its antidote, will sap the very springs of life. So that there is no real contradiction to ch. 1:8–10, 2:2, where this very falling into sin of the child of God is asserted and the remedy prescribed.
In conclusion, the grammatical contrasts between Hebrews 6:6 and 1 Jn 3:9 appear parallel in the strict sense: i.e., one is “not capable” or one “cannot.” The idea here is a flat blanket statement of propositional truth. However, one must turn to the wider literary context of First John in order to understand an additional nuance of meaning relating to the absolute source of power over sin. The power is therefore not in the Christian but something beyond the Christian. That absolute source of power is the “seed,” which provides for the new birth, or eternal life (compare 1 John 3:9 with Titus 3:5-6). In this respect, the absolute meaning of “not able to sin” may include the wider idea of permanent and absolute separation from spiritual death (because the water of the new birth “washes away” spiritual death). Spiritual death is evident through sin according to 1 Jn 3:14-15.*
* Thus the body of the believer still carries the “law of sin” (Rom 7:23-25), because of the curse to the ground (Gen 3:17). That is, the believer is still the biological descendent of Adam, whose sin precipitated the curse to the ground and spiritual death. The latter is removed only through the new birth, and the former is removed only through resurrection. The Christian therefore has permanent and absolute separation from spiritual death at the current time, and thus access to absolute power over sin (1 John 3:9), but the same Christian still remains in the body, which is comprised of the dust of the [cursed] ground.
Alford, Henry (1976). Alford’s Greek Testament: An Exegetical and Critical Commentary (Vol. 4). Grand Rapids: Guardian Press, 465-466.