Why does a divorced non-Catholic wanting to marry a Catholic need a Declaration of Nullity?
The reason is a simple one. Because the Catholic Church holds a marriage to be of significant value, it recognizes all marriages.
The covenant of marriage “is brought about through the consent of the parties, legitimately manifested between persons who are capable according to law of giving consent; no human power can replace this consent” (can. 1057 §1). In other words, it is consent that makes marriage; not the presence of a priest or deacon (though for Catholics this is necessary), not the civil license, not the permission of parents, etc.
Thus, if the person were Jewish, Muslim, Hindu or whatever, if they were married, we presume the marriage to be valid unless proven otherwise. Because a person is allowed only one valid sacramental marriage, unless the spouse dies, a Declaration of Nullity is needed or the person would be guilty of bigamy.
Everyone has a right to petition for a Declaration of Nullity, although, no one has a right to an affirmative decision. This is why it is often best to communicate with a priest or a member of the local Tribunal for guidance in completing the proper petition form.
Here is a link to one diocese’s FAQ regarding the petitions for annulments and the process: Document for pdfs (dwc.org)