At what point did military offense completely out-class military defense? The shield used to be a vital part of war, but now there's no such thing as a shield that can defend against nuclear bombs.

You really need to specify here because, well, this is once again one of those tricky situations where "it depends" comes into play. Do you mean tactically or operationally or strategically? By that I mean do you mean tactical offense (ie: small scale, men fighting on the battlefield), operational offense (the conduct and choices made by fielded armies), or strategic offense (the choices made by the State in their overall conduct of the war).

These all have very separate answers and, depending on the military historian, may completely reject your assumption altogether. Even if you mean tactically we need to discuss further; do you mean offense in the sense of what weapons a soldier is using and how they are using it or do you mean how a group of soldiers conduct themselves with respect to another.

While we wait for your response to the above we can tackle your example; the history of shields as it serves a good demonstration point of what I'm talking about above. Notice as the Medieval Era goes on shields all but begin to disappear in lieu of enormous pike formations. Would you say "offense outclassed defense"? If you only looked at the shield, yes, but that's mostly because body armor began to make shields redundant.

If you want to say the rise of the firearm, which made armor irrelevant altogether, is the end of "the defense" we have to tussle there as well. Notably the presumption that anything with shields and armor is inherently defensive warfare. It also dictates that all post-firearms warfare is inherently offensive oriented. However we can look at just basic early Roman tactics and note that they are inherently shock, offensive oriented. We can look at the initial manifestation of musketry in warfare, the Tercio and knockoffs of them, and they are inherently tactically conservative formations of slow moving, self covering, methodical movements.

Ultimately there is too much ebb and flow. The period from after the 30 Years' War and to the French Revolution is commonly known as an age of incredibly indecisive warfare, notably on the Operational and Strategic levels. Armies were just far too valuable. Yet even within the context of the French Revolution defensive tactics worked often, defensive operational and strategic plans were used, and they were used to effect.

Ultimately I reject the premise of this question altogether. I'd love to hear some answers from others, especially if they were to disagree, but I just find the premise that offense has "completely" outclassed defense as nonsensical. There are shields against modern missiles and ICBM's; the U.S. has some very advanced stuff and has had it for a while that targets and destroys the delivery system of missiles. We have interceptor rounds on top of that. There are planes which send bombs to the ground and there are installations and vehicles which shoot missiles and projectiles at these planes and helicopters. Now if you want to say flak guns, anti-missile interceptors, flares, machine gun entrenchments, and so forth aren't "defensive tools" because they go boom then we have a fundamental disagreement of what defensive oriented military tools are.