I just like U-Boats (I built two as models when I was young) and the technical aspect of the whole thing as well as history of submarines.
And I play the game (SH3) for the reason I can command a boat myself which is rather problematic in reality... it is the same as some people play FlightSims etc.
But I also like the "fight"-theme:
sneak up the enemy... set up my target..shoot... wait...bang! *cheers*
And then try to get out of there... "alife" -oh oh ... thrill - tactic - strategy etc.
If someone would ask me to analyse this I would say it is some kind of satisfaction of old prehistorical mental schemes.
What I also like about SH3 is the way one can and has to manage his crew... and the possibilty to upgrade and earn stuff.
... and of course:
Very big upgrade from SilentService2
GWX blew it up even more
OLC's GUI and some other mods add the last bit to get max realism out of it
the great community