Societal pressure, really. I can't imagine any other reason why people would get married in modern times, anyway. It's never exactly been a very functional experience, at least in the way we would prefer to imagine it. The main reason why the divorce rate is much higher in modern times than in prior times is because women have more rights/social acceptance than they used to hold, and therefore can divorce without much of the social stigma that existed previously. Of course, extra-marital affairs have existed since the times of the old aristocracy (and before), predominantly on the male side, but among aristocrats also openly on the female side (see Émilie du Châtelet and her husband, Marquis Florent-Claude du Chastellet-Lomont. The Marquis du Chastellet had affairs, and his wife, la Marquise du Châtelet, had affairs with prominent men, among them the philosophe Voltaire and the poet Jean-François de Saint-Lambert).
Fathering "illegitimate" children <i>a la</i> Arnold has, of course, been something which has been part of human life since time immemorial. However, in the scope of society's structure, it is inconvenient to do such a thing in financial terms, which is why children born out of wedlock or through affairs have historically been shunned by their fathers, as the discovery of their very existence could prove disastrous to the family ties the father's "legitimate" union helped bring about, along with any social/political/economic benefits gained from said union.
Nowadays, the rationale for keeping things secret is to appeal to the moral values of society, a far less understandable cause. Although religion and society were big factors in times prior as well (usually unfairly stacked against infidelity by women), they were not the sole factors which called for the secrecy behind the origin of so-called illegitimate children.
With that said, I can't believe Schwarzenegger's mistress went through with the pregnancy. Had I been in her place, I would have gotten an abortion ASAP. Actually, had I been in her place, I would have never slept with Arnold. I'm sorry guys, but The Terminator is butt ugly™.