Contraception has everything to do with all of those things. Indeed, the entire purpose of contraception is to "delay life milestones" of getting married and having children, both for men and for women. It's a well established empirical fact that the contraceptive pill's advent in the 1960s caused women, especially university-educated women, to marry later, particularly from the 1970s onwards. It obviously also caused them to have children later; women on the pill could choose when they wanted to have children.
Correlation /= causation.
Sexual freedom is certainly a boon from contraception (both men and women, women are not the only beneficiary of the pill from a contraception standpoint), but that still doesn't explain delayed marriages unless you think women were getting married earlier in the past because they were getting knocked up. As I said then, just like now, the vast majority of people get married before having children, not after. Also even now most couples use contraception to be free of children for years after marriage, or in other words people don't get married solely to raise children.
The only affect children have on women and marriage is that 1.) having children is no longer considered an end all be all life milestone hence there is less emphasis on knocking that out before or in place of other things and 2.) for health an biological reasons women are still pressured to have kids before a certain point, but that point is continuously pushed back by medical advances.
So no, contraception does not explain marrying later (as if it is women solely driving this phenomenon in the first place)
Women can now choose to go to university and pursue a career of their own, instead of getting married and having children.
That would mean access to education is the driver of later marriage, not contraception.
More women in employment, and especially more women with a university education, meant that the job market tightened, competition for work increased, so men had to (a) get more education than before to remain competitive, and (b) work for less money. Both of these things mean that other milestones have to be pushed back, too, such as buying a house, being promoted to a management position, or retiring. Men achieving their milestones later is a direct corollary of women being able to achieve their milestones at all. And we're all better off for it, too.
Agreed, but also has nothing to do with contraception.
There are obviously other factors, such as the decline of manufacturing, or the increase in the cost of homeownership, but the biggest one by far is the ability for women to delay childbirth and pursue careers of their own.
Pursue careers of their own, sure, but delaying childbirth not at all. Again, unless you can prove there was a significant portion of women having children prior to marriage and that thus drove them to get married you are not showing a cause and effect relationship. Women got married and had kids (overwhelming planned) because that was their primary milestone back then. That is no longer the primary milestone, thus they don't tackle it as early as they once did.
Note that having kids earlier in the past was also a MALE milestone as well, the age of fatherhood has slipped back along with that of motherhood, and there is nothing to suggest this is driven entirely by the choices of women. For instance in my relationship I am the one that doesn't want kids right now, my significant other would have three of four rug rats right now if it were up to her.