My train of thought...

ok, this is how I think about about what muscle groups to train on each day...well just a few, anyway

Alright, when working Chest, Doesn't it make sence to also work tricepts the same day since they are basically being utilized heavily during Bench/dumbell presses anyway?

Also, To work Bicepts the same day as back since it once again is being utilized heavily when doing Pullups/Pulldowns, rows...etc?

Seems more effective than a system of back then chest then arms day(in any order)

this is always how I've organized things for the past 8 years...if i'm doing it all wrong, oh well, it works for me

Thats what i use as well(push/pull) 99 percent of the time. I have tried the workout where you do Chest/bi then Back/tri but i feel my muscles arent getting enuff rest and my core lifts strugle(bench/lat pull down/rows) because im working push and pull muscles ever time i workout. not sure exaclty wht this post does for you except confirm that the push/pull method i belive is the most used, and def works the best IMO

thats what makes sense to me also

That way works. There's other ways to do it to though. You just mix it up a little.

just do what works for you. Who is to say whats right and wrong.

Currently:
Monday-Chest/Tris
Tuesday-Off
Wensday-Back/Bis
Thursday-Shoulders/Traps
Friday-Legs
Saturday-Off
Sunday-Off

Rinse and Repeat

It makes sense to me, and works for, thats how I roll.