the church doesn't allow divorce. when it's said the church doesn't believe in it, that means it doesn't believe it exists. it can't allow what's not possible.

an anullment is a conclusion and declaration that even tho a wedding was performed, no sacramental marriage occurred.

one of the things that might make it confusing is that the evaluators might look for a civil divorce. but you see, there isn't perfect congruity between the civil and religious notions of divorce.

here is a link that goes over the basic ideas. it talks about the status of children also.

excerpts:

For a marriage to be valid — for it to be something "God has joined together" — a couple needs to...

1. Be able to exchange consent, and do so freely and unconditionally
2. Consent to fidelity, indissolubility, and openness to children
3. Not have any impediments to marriage (see below)
4. Follow the sacrament properly

also:

Some common reasons for annulment in the Catholic Church are:

1. At least one partner didn't fully & freely consent.
2. Someone wasn't mature enough to understand the full extent of what they were doing.
3. There was never intent to be faithful.
4. One or both partners did not intend to be open to children.

i'll note when you hear of couples being "married for years" and being granted an annulment - that's a statement not quite properly put. they were living "as if married" for years, if an annulment was declared.

i'd say both the bible and theological reasoning. the link notes the scriptural verses.

i think what the church has to say about marriage very interesting. there's a lot more it has to say. for example, you have three grades of marriage, if you will, or three approaches to the topic. civil law, natural marriage, sacramental marriage. sometimes people will think that because they weren't married in the church they aren't married - so like they could get a civil divorce for this supposedly non-marriage marriage and then get married in the church without an annulment. but this is not the case. for a sacramental marriage to occur, you only truly need the bride, groom, and a witness. the bride and groom act as the ministers. normally the witness would be a priest. catholics are obliged to have a priest act as witness, but this is not a sacramental condition.

i also find it interesting because, well, the spouses will have a personal relationship of course, bu marriage is beyond that. my parents were married until death do us part. they didn't really get along on a personal level, but they "stayed married" - and in the end, they had a love story that achieved greatness in all honesty.