Why should [not wearing make-up] make me feel inadequate? Why should I feel pressured into fitting what society deems to be a suitable way for me to look and behave in order to be a proper woman?
Because you are a female descendant of a bi-pedal, forward vision, pack-hunting, band of primates consisting of two in-group hierarchies based on gender where rank within a gender specific hierarchy, and band rank as well, is displayed by social signaling. Being "well groomed" is one such signal. Thanks to multi-billions of dollars, pounds, euros being spent on propaganda advertising by the cosmetic companies, et.al., being "well groomed" means wearing make-up.
Can you, or can you not, become a Martian?
(LOL)
Our genetic inheritance is strongly indicative but it is NOT determinative. At the molecular biology level environmental and mental processes affect and effect our behavior. The way we "feel" about things releases hormones (proteins) that changes the way the axion hillock and axion terminals ... uh ... "work" giving the potential to eventually changing the way we "feel" about things. Psycho-and-neurological pharmaceuticals are all about affecting this directly; clinical psychology is all about affecting it, from a molecular biology POV, indirectly.
The human Central Nervous System is plastic but it's not a bunch of goo to shape anyway we wish. Further, analysis and description(s) of the "average" human CNS, including the brain, is "average" thus indicative, but not determinative, of any individual.
As I've written before, and Mig has quoted elsewhere in this diary, individual humans seek group acceptance thus group compliance and undergo stress when either is frustrated, for some individually assigned value of "frustrated." And frustration leads to stress which leads to a whole bunch of things, one of which can be a feeling of inadequacy roughly approximate to their assigned value of frustration.
OK, anyone "feeling" inadequate long enough, with a high (enough) weight assigned to the "feeling," implies that person will "become" - personal sense of Being of - inadequate roughly approximate to the weight assigned to the frustration level. This the general outline of the process and WILL vary according to the individual, their psycho-epistemology, gender, biology, previous social stimulus, what degree of acceptance of previous social stimulus, & so on and so forth blah, blah, yadda-yadda-yadda.
In the light of current knowledge -- which ain't all that great.
Despite that, it IS possible to firmly, completely, and irrevocably state: You HAVEN'T failed nor are you a failure.
You're differently normal.
;-)