All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The hadith mentioned in the question is authentic and was cited by Imam Ahmad and Imam Al-Bukhaari in his book Al-Adab Al-Mufrad. The fact that something is mentioned as a sign of the Hour does not necessarily mean that it is blameworthy. The mission of the Prophet, sallallaahu ‘alayhi wa sallam, is one of the signs of the Hour; He said, "Count six signs that indicate the approach of the Hour: my death, then the conquest of Jerusalem, etc." [Al-Bukhaari] There is no doubt that his mission is a source of goodness and light for mankind and mercy for the worlds. Likewise, the conquest of Jerusalem was a source of goodness and light.
The same applies to the spread of 'using the pen', or 'spread of knowledge' in another version of the hadith. This is one of the signs indicating the approach of the Hour, and it does not mean that the use of the pen is prohibited. The same applies to the wife's help for her husband in trade; this is not prohibited in Islam. The Prophet, sallallaahu ‘alayhi wa sallam, used to trade with the money of his wife Khadeejah, may Allah be pleased with her, before his mission started.
In his book Fiqh Ashraat As-Saaʻah (Understanding the Signs of the Hour), Shaykh Muhammad Ismaaʻeel Al-Muqaddim wrote, "Know – may Allah have mercy on you – that the fact that something is among the signs of the Hour does not necessarily mean assigning a ruling to it; the signs of the Hour include the prohibited, the lawful, the good, and the bad. The ruling should be derived from another source of evidence..."
The increasing number of women is one of the signs of the Hour. The Prophet, sallallaahu ‘alayhi wa sallam, said, "The Hour (Last Day) will not be established until religious knowledge is taken away (by the death of scholars), general ignorance (of religion) spreads, men will decrease in number, and women will increase in number to the extent that for fifty women there will only be one male guardian." [Ahmad] However, this does not mean that Islam perceives women as a source of evil or misfortune. On the contrary, Islam holds women in a remarkably refined status and teaches honoring and respecting them as equals to their male counterparts. Allah, the Exalted, says (what means): {O mankind, indeed We have created you from male and female and made you peoples and tribes...} [Quran 49:13] The Prophet, sallallaahu ‘alayhi wa sallam, said, "Women are the counterparts of men." [Abu Daawood and At-Tirmithi]
In Islam, women are men's counterparts. Both are regarded as equals in terms of religious duties and promised rewards; Allah, the Exalted, says (what means): {And whoever does righteous deeds, whether male or female, while being a believer – those will enter Paradise and will not be wronged, (even as much as) the speck on a date seed.} [Quran 4:124]
Islam accords great respect to women and prescribes the preservation and protection of women's honor by deeming it strictly prohibited to slander or defame them, warning against the severe punishment for that sin; Allah, the Exalted, says (what means): {And those who accuse chaste women and then do not produce four witnesses – lash them with eighty lashes and do not accept from them testimony ever after. And those are the defiantly disobedient.} [Quran 24:4] The Quran also underlines that the birth of a baby girl is a great blessing, mentioned in the Quran before the birth of a baby boy. It is also prescribed to hold the ʻAqeeqah feast celebrating the birth of the female just as it is prescribed for celebrating the birth of a male. Allah, the Exalted, says (what means): {To Allah belongs the dominion of the heavens and the earth; He creates what he wills. He gives to whom He wills female (children), and He gives to whom He wills males. Or He makes them (both) males and females, and He renders whom He wills barren. Indeed, He is Knowing and Competent.} [Quran 42:49-50] In addition, (anyone) raising a female child is promised a great reward and virtue that is not mentioned in relation to raising a male child. The Prophet, sallallaahu ‘alayhi wa sallam, said, "Whoever raises two girls until they reach adulthood will be with me in Paradise like this," and he joined his index and middle finger with a slight gap between them. [Muslim] The version cited by Ibn Maajah with an authentic chain of narration reads, "Whoever has three daughters and is patient towards them, feeds them, gives them to drink, and clothes them from his riches, they will be a shield for him from the Fire on the Day of Resurrection." The version cited by At-Tirmithi reads, "Whoever has three daughters, or three sisters, or two daughters, or two sisters, and he treats them kindly and fears Allah regarding them, he shall be admitted to Paradise." The Prophet, sallallaahu ‘alayhi wa sallam, also said, "If anyone is blessed with a female child and does not bury her alive or slight her or prefer his male children over her, Allah will admit him into Paradise." [Imam Ahmad] In the Farewell Hajj, the Prophet, sallallaahu ‘alayhi wa sallam, said, "Fear Allah regarding women; you have taken them as a trust from Allah." [Abu Daawood]
In Islam, the woman is the mother, whose right is the greatest right after the right of Allah and the right of His Messenger. The Prophet, sallallaahu ‘alayhi wa sallam, was asked, "O Messenger of Allah, which of the people has most right to my good companionship?" He replied, "Your mother..." The woman is also the wife, whom Allah commanded the husband to be kind to; Allah, the Exalted, says (what means): {And live with them in kindness.} [Quran 4:19] Rather, the Prophet, sallallaahu ‘alayhi wa sallam, made the standard of a man's goodness his kindness to women. He, sallallaahu ‘alayhi wa sallam, said, "The best of you are those who are best (the kindest) to their womenfolk."
The woman in Islam is not a source of evil and misfortune. Rather, all evil lies in her being distant from Allah, the Exalted, like that woman who neglects the obligation of the hijab, displays her beauty and adornment before non-Mahrams (permanently unmarriageable kin), and goes out of her house spreading sin and killing virtue. Likewise, all evil lies in the man who is distant from Allah.
Allah knows best.