@student2,
You will need to define your terms better "old times" - what the hell is that? The 20th century? The 19th? Medieval times? Ancient Rome?
Here are some general statements to go along with your general questions.
1) Women over the age of 18 (and often over the age of 12 or so) were married and there was no birth control. You do the math - and pregnancy was a fatal condition a lot more frequently than it is now.
2) They were paid **** so it was more practical to send your husband or son out to work (and work was different from now; go back to medieval times and people were often not paid at all and instead were just allowed to live on and work the land in exchange for a lord's dubious protection)
3) Look up dower laws. Go back only to the 19th century in England and America and a married woman's property, inheritance, and earnings all belonged to her husband. So you might not be seeing evidence of women working but they were; they just couldn't keep their earnings.
4) Also related to dower - you want to know why men wanted sons and not daughters? It was not just to work the land; it was also because sons were cheaper. Marry your son off and get a dowry gift from the bride's family. Marry your daughter off and you have to provide an expensive dowry - and girls' chastity had to be protected whereas no one gave a damn when it came to boys.
5) They were denied educational opportunities. Women didn't start being able to go to medical school or law school until the 19th century in at least England and the US.
6) Sexism, pure and simple. They may have wanted to work or at least earn and were unable to do so because no one would hire them.
7) And finally, what you are calling 'household' work was different and more different the further you go back. Today it's cooking and cleaning and child care. In Victorian times, a poor woman would also be sharecropping (called the cottier class in England). They would be caring for animals (having a horse was like owning a car) and helping repair the roof if necessary. Look at women pioneers. They did all of that and often delivered each others' babies, too.