I'll defer to those who are more familiar with English law and can offer a little bit of context related to the kind of jurist he was but can shed some light on some of his more notorious rulings. We don't know why this was such an important issue to him but it's safe to say Mr. Hale had some very strong opinions regarding women's role in society and how the law should interpret that role. He was born in 1609 and served as a judge and jurist, offering opinions on laws and rulings as well as making rulings of his own. According to several biographies, he was deeply shaped by his faith and viewed everything through a religious lens. From Lord Hale, Witches, and Rape (1978) in a section called "Lord Hale: A Pious Misogynist":

Hale's thinking was overpowered by a heavy burden of uncritical religiosity. Richard Baxter tells us that when a horse that Hale was riding on the Sabbath became lamed, Hale took this as a sign of divine displeasure and never profaned the holy day again. Hale's youthful conceptions of faith never grew or broadened, Gerald Hurst notes. He disliked all music. He hated intoning in church, and for thirty-six years, it is said, he never missed going twice to church every Sunday, all matters which led Hurst to an acid summary judgment: "Thus, his endurance matched his piety".

As mentioned in the megapost about abortion in America, the reason that the reference to Hale raised so many red flags is that he was the first jurist in the English-speaking world to establish the legal precedent a wife could not refuse to have sex with her husband. Known as the "marital rape exception", the ruling read:

For the husband cannot be guilty of a rape committed by himself upon his lawful wife for by their mutual matrimonial consent and contract the wife hath given up herself in this kind unto her husband which she cannot retract.

In effect, his ruling and writing encouraged other jurists and lawmakers to see married women as an extension of their husband; her body was not her own for reasons related to what Hale seemingly saw as the so-called natural order of life. His other rulings also shaped English and American law related to rape in general. Basically, Hale was instrumental in establishing both the legal and mental model that a woman's accusation of rape should be in doubt from the get-go. In other words, rather than assuming she's telling the truth, the courts should work to ensure that the man's reputation isn't besmirched until there's overwhelming evidence that he committed the crime. (Modern day philosopher Kate Manne describes this mental model as himpathy.)

To borrow again from 1978 piece:

Hale's cautionary rule, that rape charges are easy to make and hard to defend has enjoyed an unusually vigorous judicial existence despite, as was stressed earlier, its patent inaccuracy. During the British debates on the Sexual Offences (Amendment) Act, three different members of Parliament, as by rote, repeated Hale's shibbeloth. "It is so easy to make the allegation and so very difficult for a person to defend himself against it," said one. "It is a very easy charge to make but a difficult one to rebut," observed another. And, finally, a third M.P. pointed out, lest his colleagues might have forgotten: "These allegations are easily made and difficult to disprove".

In the United States, appellate court judges deciding rape cases have paid continuous tribute to Hale's "impressive observations" on the subject. Hale's stricture against according ready credibility to complaints of rape has been hailed in America as an "oft-quoted observation" and a "well-known saying", and became, in the words of Justice Bazelon, "one of the most oft-quoted passages in our jurisprudence". The point is illustrated by an opinion in an 1856 California case which relied upon Lord Hale's views to support its conclusion:

There is no class of prosecutions attended with so much danger, or which afford so ample an opportunity for the free play of malice and private vengeance. In such cases the accused is almost defenceless, and Courts, in view of the facility with which charges of this character may be invented and maintained, have been strict in laying down the rule which should govern the jury in their finding.

His views on married women influenced how he viewed unmarried women, including those who were widowed. He saw them as something unnatural or suspicious; a view that culminated in a death sentence handed down to two women, Rose Cullender and Amy Duny.

Which is to say, when pulling together history to explain a roll back of rights for women in 2022, Judge Alito turned to the words of a man who said women should not be believed when they accuse a man of rape, a man cannot rape his wife, and women who are witches should be put to death.