The
Star Trek Writers/Directors Guide (Third Revision, April 17, 1967) possibly describes the original motivation for the resistance to the idea of Starfleet being a military:
Is the starship U.S.S. Enterprise a military vessel?
Yes, but only semi-military in practice -- omitting features which are heavily authoritarian. For example, we are not aware of "officers" and "enlisted men" categories. And we avoid saluting and other annoying medieval leftovers. On the other hand, we do keep a flavor of Naval usage and terminology to help encourage believability and identification by the audience. After all, our own Navy today still retains remnants of tradition known to Nelson and Drake.
This implies that Starfleet wants to portray itself as an organization that has "evolved" beyond a military by omitting "annoying medieval leftovers" like saluting, among other "heavily authoritarian" features. None of the examples have to do with making Starfleet vessels less armed and armoured than a military fleet; none have to do with Starfleet members being less trained for combat.
There is no dictionary available from the
Star Trek universe to check the formal definition of a military by the Federation standards. Luckily, we do have a time period when Starfleet and a military organization from the United Earth called MACO existed at the same time.
MACOs were foot soldiers with traditional military features; they did not have their own fleet of starships. This indicates that Starfleet's idea of a military is defined by "heavily authoritarian" and "annoying medieval leftover" features like saluting; not the training, firepower and defence of the Federation.
This, finally, reveals the absurdity of such a definition when combined with the fact that Starfleet is a heavily armed force and the only organization that fights the Federation's wars.