What I am saying is that in terms of what Starfleet's official standing is that it is as a branch first and foremost devoted to exploration and diplomacy with.defence as a secondary function (yet still of high importance)
Which, whilst true, in no way invalidates the "military" label, they are an organisation which focuses on exploration when it is possible and pragmatic to do so, defence when expediency calls. Much like most real world militaries.
The fact is there's a fine dividing line between
1) starfleet not being a military
versus
2) sarfleet not being acknowledged as a military
Either could be accepted as canon if we look purely at the pronouncements, but actually watching the show gives us a clear and extensive picture of an organisation that in no discernable way differs from a military. For reasons we have some insight into irl (and can guess at in universe) the word "military" is perceived as being distasteful in the 23rd/24th centuries and is thus actively avoided by SF.
This can apprropiately taken as political correctness at best, propaganda or even thought policing at worst, but nonetheless what we are shown is absolutely a military organisation, just one that has a policy of not using that term.
Saying Starfleet not being a military is much like Picard saying there were five lights. We could accept it, but only by denying the evidence of our eyes because we were told to.