Teamfighting
AD carries are meant to survive in teamfights not through their HP/Resistance stats but due to their safety/range. As they also happen to be 25-35% of their team's damage output, AD carries must prioritize damage over safety.
Another reason for the prioritization of damage is because additional damage items scale your DPS non-linearly. Here's a chart I made for Jinx a few months ago (before AD carry item changes in Patch 4.10):
Note: Each differently colored line in this chart represents the first item bought in a traditional build path. This chart assumes a base attack speed of 0.625 and 130% bonus minigun steroid. Also, it is assumed Stattik Shiv procs every 10 autoattacks and deals damage to only a single target (25-30dps). Bloodthirster is fully stacked.
Let's look at the blue line (BT->Berserker's Greaves->PD->LW->IE) build path that was common in early Season 4.
9200 Gold: 480 DPS13000 Gold: 930 DPSIn other words, a difference of 3800 Gold -- one item -- means a 200% increase in DPS!
This means that if you delay your build by buying resistances, at a certain point in the game the enemy AD carry might do as much as 200% more DPS than you.
Laning
As a side note, lifesteal is a commonly built on AD carries. This means the more damage you do, the more effective health you have. Building armor early forces you to buy health potions or become outsustained in lane by the enemy AD carry.
Also note that enemy supports may be AP based (Leona, Sona) and enemy marksmen may also deal hybrid damage (Corki, Kog'maw). This means building armor may not even be of use in laning phase!