Your understanding is generally inaccurate. (or at least seemed to)
A less spoken yet big topic in Italy is the “uterus for rent” (“utero in affitto”). While most media talks about the woman role, it actually goes both ways.
The explanation under the following spoiler is potentially NSFW, yet I will try to write it in the least sensitive way possible**This is an illegal practice in Italy.**It consists in a person paying another person from the opposite sex so a child can be born between the two, but raised by only the payer. Used in the case where the actual couple cannot make a child on their own (so, in the case of same-sex unions or general infertility). The person who got payed would then disappear.
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The block of the birth certificates is going against this practice.