Yes, it's the woman's body and therefore the woman's right to choose, not the man's.
This is an argument that women have absolute right over their body. They do not.
Do women have the right to choose to not have children?
Yes. If they are not ready for children they can choose not to engage in the actions that result in the creation of children. If they are truly adamant about not having children for some reason they can choose to get their tube tied. If they are unsure and do not want to follow that path, and still wish to be sexually active, then they should be aware of the consequences for that decision.
How hard is it to keep your legs shut until you are at a point that you are ready to be responsible for your actions? Plenty of women throughout history have been able to tell men "not until marriage" and not give in until she knew that she and her partner was ready. Plenty of people also go years without sex, as they focus on schooling, a career, and betterment of themselves. It's not impossible to view sex as a luxury that you can have when you are prepared to have it, like alcohol. It's called self control.
Men are universally told that if they didn't want to be held responsible they shouldn't have done it and that their actions have consequences. Women should likewise be held responsible. They should know that actions have consequences. There is no reason to impose a death penalty on a child in the womb out of selfish or petty reasons.
The law recognizes an unborn child enough to consider it homicide if it is killed by anyone other than the mother - it is not just an assault charge. That should apply to the mother as well. Perhaps the consequences of fetal homicide should not be the same as normal homicide, but there should definitely be consequences.