Iceberg Titan doesn't allow tapping a tapped creature
Iceberg Titan reads "Whenever ~ attacks, you may tap or untap target artifact or creature". However, when you take the action, you are not prompted with whether or not you'd like to tap or untap the target; it currently just defaults to doing the "opposite" of whatever state the target is in.
I believe this is a bug, as you should be allowed to tap a tapped creature or untap an untapped creature. If an opponent taps the target in response to the ability going on the stack, and you still take the action, you should then be allowed to choose tap or untap. But instead, you simply untap the target.
Iceberg Titan doesn't read "you may change an artifact or creature from tapped to untapped, or untapped to tapped". If it did, there wouldn't be an issue. Instead, this card specifically states that you may tap an artifact or creature, regardless of what state its in.
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[Deleted User] commented
You only select a target, nothing more, when the trigger goes on the stack. The choice of tapping/untapping is made on resolution, as is the choice for actually taking that action, since it is a "may" trigger. So whatever state the target is in, you can put it into the state you want. If it's put into that state as a response, you simply decline. But if you choose to take the action, you have to choose a valid option. Untapping something that's untapped is not possible as is tapping something that's already tapped.
701.21a To tap a permanent, turn it sideways from an upright position. Only untapped permanents
can be tapped.701.21b To untap a permanent, rotate it back to the upright position from a sideways position. Only
tapped permanents can be untapped