The best argument for getting married from his perspective? In my view it depends entirely on the strength of his desire to maintain not just a relationship with her, but an equal relationship.
OK, I'm musing here. Part of this is from my own experience, part of it is from my knowledge...
It's a big issue, and one that won't go away. If she wants to marry him, she's unlikely to change her mind about that - certainly not immediately - but the risk to him is she might start to think differently about his suitability. At best, she will be disappointed. At worst, he may seem diminished in her eyes by his reluctance to do what she feels is "the right thing".
If, for example, they both wanted children and she decided to go ahead regardless of marriage, essentially she would be accepting that the risk she takes, and the sacrifices she makes, might be greater than his if they were to separate. So she may feel there is an imbalance - that they are not equal.
That's what the Matrimonial Act introduces, the assumption that both partners to the marriage make an equal contribution, and their financial footing after separation should be as equal as the division of assets can achieve. That's why the division of assets is rarely 50-50 after divorce, because it takes into account any "relationship-generated disadvantage".
I accept that there are some women to whom this doesn't apply, btw - women who carry on with well-paid full-time careers after childbirth - but they are not the majority even now. Most women will find that raising a family is much easier if they take a part-time, lower paid, local jobs. That is particularly the case if he works long hours.
So she might realise that if she doesn't want to take the risk of having children without the security of marriage, she'd better start looking elsewhere. Her love for him may not diminish, but her loyalty and commitment might if she sees it isn't reciprocated, and that can have a corrosive effect.
It will also depend on their ages, her understanding of the legal position, as well as a desire for children.
She might come to the conclusion that maybe there are other men in the world who she might fall in love with, and feel loyalty and commitment to, who might also be prepared to show that love, loyalty and commitment through marriage.
So if he keeps refusing, he runs the risk of the relationship dying a slow, lingering death - as her understanding that he is not as committed to the relationship as she is becomes an issue between them.
Ultimately, if he loves her enough to want to have children with her, why would he want to refuse her the protection marriage provides in the event of a divorce?