My understanding of oppression is that the oppressed group must have something the oppressor wants - in the case of women that's reproductive >labour. If women were not the sex uniquely able to gestate, birth and nurse children, they'd be no oppression.

I know this is a common view, but I think it's only part of the picture. Males also oppress women because most males are heterosexual and from about age 11-12 on het males spend a good deal of their lives consumed by strong, compelling sexual desire for females. Het males see females as the vehicles through which they can obtain the greatest of all pleasures - the range of delicious, intoxicating, overwhelming physical sensations that come from sexual contact and closeness, and which culminate in orgasm. Pursuit of that sexual pleasure for its own sake is a major instinctual driving force in all humans past puberty, but is an especially strong driving force in male humans.

Most males when they seek out females for sex are not desiring to impregnate us or to make us bear their children - males are focused on their momentary, short-term sexual pleasure, and on their pleasure alone. Often, in fact more often than not, thoughts of making use of us females for our reproductive capabilities are the furthest things from their minds. Their minds are not filled with thoughts of how to rope us into gestating, birthing and nursing children or figuring out how to make sure our children are theirs as well. Most of the times when men want sex, which is most of the time for a good part of their lives, they do not want to pro-create. Their minds are focused solely on getting their dicks inside us and shooting their wads for all the delicious pleasurable sensations it brings them right now in the moment - not on all or any of the consequences for us female people that could transpire from that action.

IMO, men oppress women because they want girls and women to make their willies and the rest of their bodies feel good - and this is just as important, perhaps more so, than men's desire to be able to claim and have dominion over the children we bear. After all, men who used to have huge hordes of sex slaves kept in harems often had no problem killing off many of the offspring the women they held as sex slaves bore shortly after birth; these men valued the women they enslaved for sex primarily for the pleasure they could provide, not necessarily for their fecundity and "reproductive labor."

Another reason males oppress women is that the biological differences between the sexes makes it easy for them to do so. Nature has endowed males with huge advantages in strength, speed, sturdiness and (usually) size over females - and has equipped girls and women with physical vulnerabilities and disadvantages that males don't have, which make us easy/easier prey, as it were.

Of course, there's no reason that physical power imbalances between different humans must always lead to dominance and subjugation and oppression; most adults' instinctive reaction to babies - and to the weak and frail - is to care for them, not to oppress, abuse or limit and deprive them. So there's nothing written in stone that says males have to exploit their physical advantages over females to oppress us - the desire to oppress must be there first. And the secret to that desire is in the minds and psychology of males. Which takes us back to the issue of male sexual desire and the massive part it plays in boys' and men's lives from the dawn of puberty on.