But this is AARe not LHTR.
But AARE clearly defers to LHTR if you read the rules.
So why should the submarine be allowed to move from SZ 52 to SZ 60 (in the case of my example) to attack more units when a destroyer is present in SZ 52? We certainly wouldn’t allow a submarine from SZ 55 to attack in SZ 45 if an enemy destroyer was present in SZ 52 without at least giving the destroyer a chance to detect the submarine.
I already told you why.
First, there is the logical contradiction - why do you pick on subs? For instance, a destroyer would be stopped by another destroyer if it ran into it along the way, so if there is a destroyer starting in an enemy zone, can it not run away either without fighting?
Second, LHTR clearly states that you can make a combat move out of a seazone which is enemy occupied at the beginning of your turn. You only resolve combat (i.e. roll dice and attack/defend) if your combat move ends in a contested area (or aa guns along the way, but that is irrelevant). Since the sub’s combat move does not end in a contested area, then there is no resolution of combat. There is no firing, and in the case of AARE, there is no detection roll. Of course, the sub could choose to stay and fight, but there is nothing in the rules to suggest that naval ships are forced to fire if they started in a contested zone.
Third, there is a very big distinction you are not making in your example. The distinction is whether the sub is attempting to move into a seazone occupied by a destroyer - or if it already started in a seazone occupied and decides to move away. Think of it this way; if in Monopoly you land on Go or pass Go then you collect $200 dollars (if you land on a destroyer or try to pass the destroyer then you have to stop and fight it). But if at the beginning of your turn you are on Go, you do not again collect $200, you roll to move on (if you start in a zone with a destroyer, you do not have to fight, you can run away).
If this is still too confusing, think of it like this: in AAR destroyers detect on a 6. I.E., they always immediately detect subs. Yet that does not prevent the sub from running away like other naval units if at the beginning of the turn the sub started in a contested seazone with a destroyer in it. The only difference in AARE is that destroyers detect on a 3 (without techs or support). Detecting on a 3 has nothing to do with them being able to run away like the situation states, because detecting on a 6 also has nothing to do with them being able to run away.