Milk seal didn't break
It happens sometimes, no worries.

It could be the perforations that make the band break off were not quite cut correctly, could be the band was just a hair wider than normal (or the plastic softer), could be the neck of the jug was just a bit narrower.  All within manufacturing tolerances.  

Usually, if you pick at the separated band, you can pry it off the milk-jug neck, its not even that hard.  That is essentially all that happened with your jug, the perforations didn't tear when the cap was removed, so the band got yanked off with the cap - probably part of why it wasn't as easy to open, you needed the extra strength to stretch the band loose.  

The breakaway band doesn't have anything to do with the milk being "technically sealed" or still sealed or not, the important seal was the airtight suction between the cap and the milk that kept the milk form exposure to air.  If that seal was good, then the milk is safe and the band not breaking off isn't a problem.  The lid is supposed to be a fairly good cap anyway, to keep the milk fresh while being used.  

The band doesn't actually make a difference after the initial opening, it's just supposed to make sure you know the milk wasn't opened before that, during shipping or whatever, maybe prevent the cap from working its way loose or letting you know if it had. 

You might want to remove the band if it makes re-capping your milk difficult, but otherwise - it isn't a problem.