AT&T Fiber Optic Line runs in front of my property - why can't i get internet access with it?

Most likely not a residential fiber. Destined for a cell tower or emergency services I see no terminals so pretty sure that’s what it is 

what does a terminal look like? because there is a small box attached to the line at another post along our property.

No

That box is a copper terminal for phone.... normally splice cases are round not rectangular. 

note in the pic below, the aerial copper terminal is to the left of the pole while the fiber terminal (fingers pointing down at angle) is to the right of the pole.

In the next pic aerial splice case on the line with copper telco terminal on the pole...

ok. thanks for the clarification. figure i couldn't leave any stone unturned so had to ask. oh well.. i guess i keep waiting then. thx!

The box on the line is probably an old linear splice case and not a copper terminal. Copper terminals are generally huge. Its probably like they said, going to Police/fire or government in general or to a cell tower or many cell towers. Basically AT&T COULD very easily plan an outage and redirect this traffic, then upgrade this route to wavelength services and free up hundreds of fibers on this line and then install a splice case and give you internet but they really hate customers and money but more importantly whoever is providing you with internet is already paying them for using a portion of the network so either way their still getting paid off your access somewhere somehow. Also AT&T hates work.

Do we really need to keep digging up 3 year old threads?