The explanations so far pretty much cover the basis for giving women the choice. What is lacking is the same degree of freedom for men. Sadly, even shockingly often, men end up becoming fathers in spite of not wanting to if/when on the other hand the woman wants to become pregnant. Women have the Pill, the morning after pill, abortion and sterilisation. Men have sterilisation, or the condom which half a century and more ago was better than nothing but is woefully behind women's options. Make no mistake, if men had the option of contraception as effective as women's then we would see a significant change in things, including at least a temporary drop in the birth rate in many countries, including the UK until women ensured they had a Yes from the man so he releases his fertility or else women in significant numbers switched to sperm banks.
Some have a conspiracy theory to explain why the male contraceptive methods so far developed and found effective have not reached market years later. Women are at a distinct advantage in these matters.