"ἐξ ἡμῶν ἐξῆλθαν ἀλλ’ οὐκ ἦσαν ἐξ ἡμῶν εἰ γὰρ ἐξ ἡμῶν ἦσαν μεμενήκεισαν ἂν μεθ’ ἡμῶν ἀλλ’ ἵνα φανερωθῶσιν ὅτι οὐκ εἰσὶν πάντες ἐξ ἡμῶν"
This Greek text illustrates why mere word studies are not effective. One must look at the syntax. There are verbs associated with these reoccurrences of ἐξ ἡμῶν, see bolded above.
The first occurrence is a verb of movement, ἐξῆλθαν. This gives the sense of moving away from someone/something.
The other occurrences are all stative[a] verbs of existence, ἦσαν and εἰσὶν from είναι (to be).
So while the first sense means 'to separate from' the next three are source as in 'belonging to'.
ἐξ is a form of εκ (out of or from) and ἡμῶν is "of is." Note that the verb in the first repeats the ἐξ.
So it is not an arbitrary decision to treat the ἐξ differently as if there is some bias being introduced. In fact, assuming one invariant meaning to a preposition may be committing the root fallacy. [b]
[a] Wallace ExSyn 358–60
All is not as it seems, however. A stative preposition can occur with a verb of motion, just as a transitive preposition can occur with a stative verb. In such
instances, how are we to interpret the data? Note, for example, the uses of εις with a stative verb. εις generally has the meaning of movement into from without.
However, when it is used with a stative verb, such as θρεω, κάθομαι , εισμεν, etc.,the idea of motion is negated by the stative nature of the verb. On the other hand, pisteuvw + εν is the equivalent of πιστεύω + εις (cf. Mark 1:15; John 3:15).5 The idea is “put one’s faith into” even though εν is used.
The general principle to follow is that the verb takes priority: Stative verbs override transitive prepositions, and transitive verbs override stative prepositions. In other words, just as the preposition virtually governs the noun, so also verbs govern the
force of prepositions. There are few exceptions to this general rule.
[b] b. Root Fallacy
As lexicographers have long noted, the root meaning of a word is not necessarily an accurate guide to the meaning of the word in later literature. The same is true of morpho-syntactic categories: one ought not look for some kind of invariant meaning that is always present with the preposition. The meaning of words changes in time. Further, a word has a field of meaning rather than a point.
Such is no less true for prepositions than for other words. (ExSyn 362–63)