The above answers all raise very good points, but I want to expand a bit on what the previous answer stated. I know this question was from a while ago but I found this quite interesting. There are a lot of numbers below but at the end I've written a short piece actually answering the question.
In League of Legends items scale with other similar stats. What I mean by this is that the more armor you have, the more each point of health you buy will be worth.
For example, Say you have 100 armor and 2000hp at level 18 with runes and masteries etc. buying 50 armour and 500hp increase your effective hp (vs AD) from 4000hp to 6750hp, an increase of 1750 effective hp. Buying another 50 armor and 500hp increases your effective hp (vs AD) from 6750 to 9000hp, and increase of 2250 effective hp. As you can see, the second purchase of more armor and health gave more effective hp. This is because of the way that armor scales with health so building lots of both is more effective.
A similar thing occurs with offensive stats but even more so because there are 3 (4) stats affecting your dps, Attack Speed, Damage, and Crit chance (and Crit damage).
So if you had two champions, and they both built half offensive and half defensive, in raw total numbers they would have far less combat stats than two champions who had one build full defensive and one build full offensive. This effect is one of the reasons ADCs exist, because having a glass cannon style character and a tank will be stronger.
However in the actual game there are a lot of other points to consider, including abilities, positioning and the fact that when one character dies they stop dealing damage. Hence it is usually beneficial for the adc to build a defensive item (full build) and lifesteal to try and stay alive longer.
Aside from all the numbers above, the main reason you don't want armor early in my mind, is because once you get into teamfights you should be taking 0 damage (hence the armor is useless) and so want as much damage as possible. Your maths is valid and in laning phase I do think having defensive items actually is beneficial (especially in an adc 1v1), but it's not worth the trade off for being weaker in teamfights.