If I need up to two centimeters more length to my bike, is it better to keep the stem and get a seatpost with more setback or to keep the seatpost and get a longer stem? I don't want to change the bars, or the frame. Currently have 120mm stem and 16mm seatpost setback.

Never ever (!) Adjust reach with saddle setback. Saddle height and setback are the most important adjustments on bike fit so you don't want to mess them up.

A longer stem definitely. Also you can increase saddle handlebar reach by flipping and slamming the stem (if you are limber enough)

Why do you need 2cm more reach?

Set back is related to leg length, saddle height, and 'style' (i.e. forward position for TT).

Stem length/angle and bar reach are used to adjust reach once your saddle is positioned where you want it.

Always go BB->saddle->bars for fit. BB (and crank length), then saddle position, then bars.

How do you know you need more length?

His girlfriend said so.

Slam the stem, bend your elbows, that should give you more reach!

^^ reading idc's post after merlin is pretty funny

BTW, to the OP, I always think of the BB, saddle, and hand position as a triangle. To get a true fit, you need to dial in all three sides, balancing power/aero vs comfort (and avoiding any back and knee problems). So, don't mess with just the stem or the saddle setback. There are good fitting guides on the interweb I am sure you can read up on that will help you.

This.

We need more information though. What is the problem to be solved by "more length"?

I will say that on a larger bike (as would be more typically ridden by a 120mm+ stem user) 16mm setback might be on the low side depending on the saddle (length of rails).

Stem angle and head tube angle also factor into the stem's role in reach. I like the Brightspoke stem calculator's "compare" feature for figuring out what messing with stem height/angle do for reach.

But his wife said he's fine. So what's the guy to do?

I've learned to not change anything unless there is a problem, and only change one thing at a time - ride on it for long enough to definitely say yay or nay - and keep working towards that perfect feel. I been at this process for 2 months on my new bike and I'd say now I'm finally getting into a 100% painfree and powerful position... a pro fit might have accomplished this in 20 minutes.

Screwin with the seat can totally change the pedaling feel - this could be desirable or not - I'd get that setup first and then tackle the handlebar placement... but really its an integrated system that all has fall together just right... when "feel" is part of the equation math becomes less of a concern and then its really just up to you to change stuff until its right.

Am pretty sure you need a new bike...

Since most are given the rote 41 answer...I will give you a bit more hope other than tossing your frame.
If you want a real solid answer, post your specs:
Height
Cycling inseam...not pant inseam
Seat tube angle
Saddle height top to BB
Ideally post your saddle tip to BB center...drop a plum line from saddle tip and measure to BB. Or...take your frame reach dimension and subtract saddle to steerer centerline.

A 16mm setback post isn't much. Amateurs...I am one, many time benefit from a bit more setback than the pros. Some pros btw...6' and taller run massive setback...some on the order of 110mm + from saddle tip to BB center. This moves their big body weight and length rearward to take some of the weight off their hands as they tend to run a lot of drop.

So your answer is...it depends. If you haven't experienced with every combination of fit...you don't know. I know if I run a 16mm setback Thomson post on my bike, I will have too much weight on my hands. I need more setback to center my weight.
PS: you may want further insight as to why setback is individual...even for same size riders. There is a reason why some pros can tolerate and ride with little setback:
a. they have much greater sustained pedal pressure than amateurs which naturally unweights the hands and pushs body weight rearward.
b. a more forward saddle position opens up the hip angle which allows for greater drop and a better aero profile.

In summary, two identical riders only with different pedal force may prefer very different setback and drop...based upon a & b above. HTH.

If you already have a relatively normal stem (110-130mm), you need another bike. If it's short, get it into the sweet spot.

That's incorrect. He may end up prefer moving his saddle rearward and leave his stem length alone or...even lengthen it.
For example I ride much more setback and a 140mm stem as do many pros.

I wouldn't disagree with your statement. My personal philosophy is to find a frame that fits me and allows the use of a stem length 120-130 (I have short arms) for neutral handling. I am leery of ultrashort stems to achieve fit.

Issue is...perhaps the majority of those that ride road bikes don't know their best frame size. How do you learn your best frame size and position? By owning 20 bikes and trying every permutation of fit. Most don't go there. Those that do are rewarded by their dilligence. Position on the bike is transcendent.
The OP doesn't know if more setback will be better. None of us know until we try. Pros run from 25-120mm of saddle setback. Most of us fall somewhere in this range...and unless you test the margins and gradations in between with varying degress of reach and drop...one doesn't know whats optimal.