If the mother is still married but have a child by another man the mother can not list that man as the father. The father looses his parental rights.The mother is forced to sign a document that isn't true.
The husband is the legal father (so the mother is not falsifying any documents). The biological father can file with the court to be recognized as the father. If the parties all agree, a 3 party affidavit can be signed to change the birth certificate.
The answer to most "how can something be legal" questions is that the legislature has passed a statute. You are free to contact your legislator and request a change in the law if you want to do that.
A lawyer can draft a 3-way Acknowledgement that corrects 5he birth certificate
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