Etymology of 奴隶 (Slave)
A personal experience, most etymology explanations of characters are not definitive. Explanations can be derived from theoretic work or maybe just personal imagination.

That been said, I searched in google and found:

Figures on how 奴 as written in ancient and modern times. Link from hkbu.edu.hk. Now, please look at the figure below, which is 奴 in its 小篆 form (the character written form standardized when China was first united in Qin Dynasty after 221BC). 

As described in the same page, 奴 --> 女 + 又 --> 静坐的女性(Female seating courteously) + 手的象征 (Symbol of hands) --> Female who work with her hands (hope you can get this point from the figure below).

To go further, this explanation links 奴 to one of its main meanings -- 奴婢/奴仆/奴才, which is similar as servant or maid in English.

Here, there is nothing about the 'servitude'. But, of course, one can explain 奴 from another main meaning -- 奴隶\奴役, which means slaves or servitude.

This is really a side-proof that etymology of characters are open to ones' empirical/theoretical research or even imagination.