I can explain what you're missing. I wish there was a tl;dr, but CR is a complicated topic and while the problem you are having is not unusual, addressing it requires a great deal of exposition.
The DMG's process for developing a creature is not what defines the CR of a creature. DMG p.237 clearly states that determining CR is not merely a mathematical formula. The numeric calculation are a starting point. The actual definition of CR is in the Monster Manual (p.9). To paraphrase, a creature with a CR of X means that 4 appropriately equipped, well-rested adventurers of level X can face the creature in combat without a death.
So you do the math, then the next step is to compare the creature to PCs and determine the maximum level that PCs would have to be to face the creature in combat without reasonably expecting a death.
So looking at the Monster Manual version of the an ogre it is pretty clear that 4 1st level characters are very likely to have a death when facing the ogre. His damage (2d8+4) is going to render every 1st level PCs except a barbarian or a D10 class with a 16 Constitution unconscious with a single hit. And a high damage roll, or a crit, will kill most first level PCs in a single hit. Further, 1st level characters don't have the damage dealing abilities to deal 59 points of damage quickly. A first level PC's average damage is somewhere in the 7-8 hit point range. So they are looking at 8ish hits to take an ogre down. So it is clear that 4 1st level PCs are probably going to experience a death when facing an ogre.
So on to your situation. Having done the math, you arrive at a CR2 for your new "armored ogre". That is the first step. You have to determine if 4 appropriately equipped, well-rested 2nd level characters facing your armored ogre in combat are likely to suffer a death, and if so, you need to raise the CR. There are multiple ways to do this. You can use a qualitative approach as I did in the previous paragraph. Or you can recruit some players to pit 4 2nd level PCs against the armored ogre to see the results. Or you can pull down some pregen 2nd level characters and shadowbox it with you playing the PCs and the ogre. Or you compare your armored ogre to other CR2 & CR3 creatures to decide. How does he look compared to a bandit captain or veteran?
Because CR is complicated and such a common problem, I put together a FAQ video which may help: CR FAQ
Also, here is an example where I'm building a CR2 Death cleric, which may help: