OK, as for giving credit to Zenguitars post, and very valid inclusions of factors that can play role, I'll ask you that owns any acoustic guitar, with a nut, to proceed with the following nit picking tuning test, and it's a bit long winded but so it is (I've posted this some years back before, and some readers turned perplexed and said "wow, never thought of this before!"):
1. Bring out the most accurate tuner you have in your arsenal. Strobe or whatever.
2. With as fresh strings as possible (new ones preferably) tune up so the tuner show 0 cents deviation (none at all) in all readings on all open strings. Make sure they stay there and touch up after a while if they slack.
3. Now: PRESS down the first fret on the G string, as you would be supposed to play a G#. Press like you would play it BUT DON'T PLAY IT!
4. Now, play the OPEN A-string instead, or E-string, take a good look at what your tuner is showing for that open string. Not exaclty right on anymore? :o
5. Do this for all open string. Some, like high E and so on doesn't move at all, so some strings deviate from right on pitch and some not.
6. This is due to the nut, that you induce increased press on the nut, and moves ALL of the nut down a bit due to the wood underneath it, the glue is fleixble in spite of drying up, or that the nut is made of material that is too soft.
This is why they invent methods like Earvana nut, BFTS, True Temperament frets, yada yada yada. To shove down or throats...they do not help.
Especially nylon string guitars suffers from this, no matter how cheap or high-end. If the nut was cut in 6 individual nuts one for each string you would have no problems. But that would be kind of unwieldy, say if a string snapped, and that bit fell out from the slot.
You can do the above test again, with a capo on the first fret, and use the "open" strings then, and come back here. Same phenomenon will not happen. Also, zero fretted guitars does not suffer from this phenomenon.