In my earlier post on Didache 2, I have the following:

   οὐκ ἔσῃ διγνώμων
   Do not be double-minded
      οὐδὲ δίγλωσσος·
      or double-tongued:
         παγὶς γὰρ θανάτου ἡ διγλωσσία.
         for being double-tongued is a death trap.

   οὐκ ἔσται ὁ λόγος σου ψευδής ου κενός,
   Your speech should not be false or vain,
      ἀλλὰ μεμεστωμένος πράξει.
      but verified by action.

The first bit involves a two-sided prohibition: Don't be "double-minded" or "double-tongued"; and has further explanation: "for being double-tongued is a trap of death".

The second bit seems to reiterate the first bit: Speech shouldn't be false or vain. This has an additional positive clarification: instead, speech should be verified by action.

Thus, instead of simply prohibiting (as the first portion of section 2 does a lot of) the idea of being double-tongued/double-minded is prohibited but is also corrected with proper action specified. Instead of just not doing something and leaving it at that; the Didachist recommends that one show reliability of speech by following through and doing what is spoken.

This is powerful, at least in my reading. This isn't simply a laundry list of prohibitions. Adn this shows up again just a few words later:

   οὐ λήψῃ βουλὴν πονηρὰν
   Do not enter into evil plans
      κατὰ τοῦ πλησίον σου. 
      against your neighbor.

   οὐ μισήσεις πάντα ἄνθρωπον,
   Do not hate any man,
      ἀλλὰ οὓς μὲν ἐλέγξεις,
      but some you should correct,
      περὶ δὲ ὧν προσεύξῃ,
      some you should pray for,
      οὓς δὲ ἀγαπήσεις
      and some you should love
         ὑπὲρ τὴν ψυχήν σου.
         even more than your own life.

Here we have a short prohibition: Don't plot and scheme against your neighbor. But it is followed up with a more general prohibition and then a positive three-pronged prescription on how to instead interact with other people. Don't hate others, instead:

• correct those who need correcting
• pray
• love even more than your own life.

The Didachist isn't teaching that there are only three ways to interact, and each relationship we have will be classified exclusively and accordingly (e.g., I correct Fred, I pray for Miguel, and Gino is someone I consciously show Christian love toward). This is not a three-point sermon in ordering relationships in a positive, Godly way. Instead, the Didachist is offering suggestions to use in each and every relationship, whether a next-door neighbor, friend, co-worker or shopkeeper. Some relationships may exhibit one, two or all three of these sorts of interactions. Some may require more.

As far as the Didache goes, however, this way of expressing the prohibition with negative statements and then following up with a positive prescription on how one is to act is helpful and logical, particularly if the Didache was originally a treatise for the baptismal candidate. The formula seems like:

• Don't do something. [negative prohibition]
• Restatement and generalisation of the prohibition.
• Do this instead: [positive prescription]

At least, that's what I noticed in re-reading the section this afternoon. YMMV.