Why build armor when you fall behind?

I see this advice offered all the time as a no-brainer, but I have yet to see the line of reasoning behind it. I can see why it makes sense: being able to stay alive longer affords you more chances to capitalize on possible mistakes the enemy team will make.

The possible counter-argument I see to this is that building armor will put you further behind by making it more difficult to net kills and catch up. However, armor is likely more important as it will allow you to defend and farm better.

But what do the people who typically offer this advice think?