"Solely" is doing a lot of work there and making a great deal of assumptions.

Yeah but that was the whole point. You're telling someone who already doesn't want kids why they should want kids, but you're giving them only one reason. If they do so, it will only be for that reason

Not necessarily. Suppose that person has multiple reasons to want kids and multiple reasons to not want kids. They analyze the pros and cons and figure that the cons slightly outweigh the pros so they choose not to have children.

If later they learn something unpleasant about nursing homes, or pension plans, or something else relevant to their expected quality of life at their old age, then that might tip the scale towards having children, even though it is only one of many reasons.

The last reason that tipped the scales towards a decision is not necessarily the only one or even the most important.