stacking defensive items has diminishing returns so for every armor item you get over the first, you get less value out of it. if she gets a damage item instead, she effectively has more value from her items than you. also, offensive items are just stronger by themselves (but also more expensive) so if both parties have 0 items, tanks are pretty tanky. if both parties have 1 similar-cost item (rapidfire gun vs deadmans plate) the tanky item wins BIG time but with every item they get, he falls behind more and more and at full build, if you get 6 tank items and the other one gets 6 damage items, you get melted instantly because his items are stronger and stack much better.
this means generally its not worth to buy more than one defensive item of a type (1 armor, 1 mr) and only if their AD damage is really insane, add a thornmail to the mix.
other than that, unless you are fed, you are just wasting too much gold.