@ Wamster
Another possibility is that he doesn't want her to be able to leave without consequences, in case she does.
Around half of all marriages end in divorce, mostly initiated by wives. Most men are aware of this from personal experience as they and their friends and colleagues get older. Probably more stay unhappily together because the parties see no alternative.
Most or probably all men are likewise broadly aware that divorces are financially bad for them - unless they marry someone much wealthier, or unless they quit work to become a house husband financially supported by their wife.
If you buy a teapot based on the salesman's claims that it also makes the tea, then what he said to get you to buy the teapot is part of the deal. If this later turns out to be untruthful, you can give back the teapot and he has to give you back the money.
This is not the case with marriage, where if one party conceals that they used to be a drug addict, or a prostitute, or a convicted criminal - or have become one subsequently - the other can get it ended, but not unravelled / annulled, and there'd rarely be any difference in the financial or child care outcome.
Most men get to observe this and many probably see this as uniquely unfair. The rate of marriages in the UK is in long term decline. I don't know of any detailed study into why, but suspect that men's rather than women's reluctance has most to do with this. If the option of living together - with children, but with reduced / no financial risk - is available to them, they take it. Same upside, less downside.
One can argue until one's blue in the face as to whether this is correct / right / immoral or whatever, but it doesn't really matter, if it's what men believe.
In Wamster's suggestion above, the risk with the list of suggestions is that it amounts to a demand for money. If it looks like her main reason for wanting to get married is so that she'll be OK at his expense if she ever feels like leaving, then in effect he probably wants not to get married for exactly the reasons that she does.
This may not be the exact case in the OP's circumstances, but I'd strongly suspect that something like the above has coloured her DH's thinking.
Which is why I suggest she needs to understand what he sees as the benefits and drawbacks of marriage to him. Not to her, not to the baby but to him. How is it good for him?
If he can't actually think of any benefits, and the drawbacks are "most marriages fail or are unhappy and you would take me to the cleaners in a divorce", then there may be more work to be done on this relationship than she yet knows.
Men will get married, because they think their marriage will be among the minority that works rather than the majority that doesn't, but some need persuading to this view.