Paul wrote that women should cover their heads in church (1 Cor. 11:2-16). Why do we not enforce that mandate?
The passage you refer to is difficult to interpret, mainly because we are not as well-informed about the topic as Paul's original readers were. Scholars have written much about this passage and its sociohistorical background, but still they disagree. A careful analysis of the verses requires much more space than I have here. So the information I provide will contribute to an answer and stimulate you to do your own research and analysis of the text.
Adventists have traditionally taken what the Bible says at face value, unless its context suggests otherwise. In some cases a biblical passage may be addressing a topic of relevance only to the original readers, such as, for instance, removing one's sandals when approaching God (Ex. 3:5), a sign of reverence and respect. There are places in the world where you have to remove your shoes before entering an Adventist church. But in the Western world we show reverence in different ways. We interpret Paul's counsel on female head covering as a cultural issue. Here are some reasons.
1. Variety of Views in the Bible: That the topic of wearing a veil is a cultural matter is suggested by the fact that during the biblical period the practice varied. In the time of the patriarchs prostitutes covered their face with a veil (Gen. 38:14, 15). Interestingly, Middle Assyrian laws (twelfth century B.C.) did not allow prostitutes to wear a veil. Much later we find some women in Israel wearing a long veil during magical or divinatory rites (Eze. 13:17-21). A bride covered her face before her wedding as a sign of modesty. Some biblical passages suggest that the wedding veil was an ornamental diaphanous veil (S. of Sol. 4:1, 3; 6:7). A veil that covered the whole face- as we find today in the Islamic world-was probably unknown in Israel. More common was the shawl placed on the head, which in some cases was a sign of humiliation and mourning, as suggested by the women depicted in the stone engravings of Sennacherib, wearing them while leaving the city of Lachish after its fall. David also covered his head in mourning (2 Sam. 15:30). No Old Testament law required women or men to wear a head covering; the social practice was simply accepted as appropriate.
2. Purpose of the Cultural Practice: Paul is not discussing the veil that covered the face of a woman, but a shawl placed on the head during worship. The use of a female head covering was common in Greek and Roman societies. Studies made about the Roman practice reveal that prostitutes were forbidden to wear one and that both women and men covered their heads during worship as a sign of reverence and piety. In fact, the shawl was part of the Greek robe, not a separate piece. Greek culture did not require men to cover their heads in worship. That was also the case among Jews. In Roman culture the female head covering was a symbol of high moral values, preservation of femininity, and commitment to the husband; wearing it brought honor to the husband and the family.
3. Reason for Paul's Counsel: Paul was promoting among Christians a social practice related to proper attire. The basic values represented by the head covering were compatible with the Christian message, and rejecting the practice could have brought discredit to the church. The wise approach was to continue to do what was practiced by Christian women before they became Christians, in order to demonstrate that Christianity supported society's high values and not moral corruption. But not all Roman women covered their heads; wealthy women were somewhat socially liberated, and it is possible that some of them became Christians and did not cover their heads in worship. Paul would have been trying to correct that attitude to protect the integrity of the community of believers.
The fact that covering the head was a cultural issue does not mean that what Paul wrote is meaningless for us. The values he was attempting to inculcate in believers are to be preserved by us and embodied in other ways. Values such as modesty, bringing honor to our families in the way we dress and act, and preserving sexual differences (gender specificity) in our appearance and demeanor are not culturally determined.