I'm blocked ...
Do you have Skyrim last version 1.5.26.0.5 and USKP 1.0 ?
Do you tried going though
all dialogue that Arngeir has available? Maybe some line is hidden (run with mouse wheel) or perhaps you don't trigger all the dialogue avaliable, some kind of preliminary question first.
Also, try to speak with him in different places (indoor / outside) at different times of day / night. Maybe the trigger depends of that
Do you have a "letter from a friend" in your inventory? Is another "source" of locations of Word Walls... Open if you have not done yet.
...Or ?find the source of power in
something? in journal (under misc quests)? Maybe you have to finish that quest first to Arngeir give you the dialogue.
You can reset Arngeir AI with console command but I think this is a to much shot in the dark ... Open console command, click in Argneir, then write
resetAI , then ?enter?
Or you can reset the quest to inicial stage with
resetquest freeformhighhrothgarA and try to talk to Argnier again.
I don't know ...

If everything fails, you can report this bug https://unofficialskyrimpatch.16bugs.com/projects/7078 and try for a solution later.