436. And they had breastplates like breastplates of iron. (9:9) This symbolically means that their arguments based on fallacies, with which they battled and prevailed, appeared to them too strong to be refuted.

Breastplates symbolize protections, because they protect the breast. Here they symbolize protections of falsities, which are concocted by arguments based on fallacies, which people use to defend a false proposition. For from a false proposition nothing but falsities can flow. If truths are advanced, they are regarded only externally or superficially, thus also sensually, and so are falsified, becoming then fallacies in the people who entertain them.

Breastplates have this symbolism because battles in the Word symbolize spiritual battles, and weapons of war therefore symbolize various defenses connected with such a battle - as in Jeremiah,

Harness the horses, and mount up, you horsemen! And station yourselves in your helmets, polish the spears, put on the cuirass. (Jeremiah 46:4)

In Isaiah,

He put on righteousness as a breastplate, and a helmet of salvation on His head. (Isaiah 59:17)

In the book of Psalms,

...under His wings you shall be confident; His truth shall be your shield and buckler. (Psalms 91:4)

And so also elsewhere, as Ezekiel 23:24; 38:4; 39:9, Nahum 2:3, Psalm. 5:12; 35:2-3.

Their breastplates being breastplates of iron means, symbolically, that their arguments seemed to them too strong to be refuted; for owing to its hardness iron symbolizes strength.

It's common to say “I see” when we understand something. And indeed, “seeing” in the Bible represents grasping and understanding spiritual things. So it makes sense that the eyes, which allow us to see, represent the intellect, which allows us to understand spiritual things. This can also be used in the negative, of course; the Bible speaks of people having eyes and refusing to see, and the Lord when He was in the world advised plucking out an offending eye. These represent a refusal to acknowledge truth, or being misled by falsity.