@Alex listed five reasons. I offer eleven more (some of which might slightly overlap but aren't explored in the same way):
- The married person lacked the mental capacity to consent to marriage which a guardian or next friend seeks to annul.
Often a court appointed guardian or parent of a person who lacks mental capacity (or is not old enough to legally marry) can seek an annulment of a marriage, but not a divorce. Often a valid marriage would revoke the appointed guardian's appointment by operation of law in favor of the spouse.
- The other spouse committed a crime or tort against the spouse seeking the annulment.
Historically, spouses had broad immunities from rape and almost all other crimes except murder, committed by a spouse against them, and was not permitted to sue a spouse for civil wrongs (i.e. torts). In more recent times, most developed countries have repealed such marital immunities. But not every jurisdiction has done so and not every jurisdiction that has repealed most marital immunities has repealed all of them.
A divorce does not abrogate marital immunities for actions that took place during the marriage, while an annulment would generally make it possible to bring criminal prosecutions or sue the other spouse for conduct that occurred during the putative marriage.
For example, maybe a boyfriend and girlfriend go on a trip to a place that does not recognize marital rape. The boyfriend gets the girlfriend drunk and drugged causing her to uncomprehendingly agree to sign a marriage certificate. The boyfriend then brutally rapes his girlfriend. If they divorce, he can't be prosecuted. If the marriage is annulled, he can be prosecuted.
- Divorce may have a waiting period that does not apply to annulment.
Usually, there is no statutory waiting period between the filing of an annulment petition and the soonest time period when it can be granted. If it is not opposed it can be granted immediately, allowing the parties, for example, to remarry immediately, and prevent the putative spouse from being the presumed parent of the child of a pregnant bride (especially when the child has another genetic father).
In contrast, there is often a mandatory waiting period (often three to twenty-four months) before a divorce can be granted.
- The other spouse may be without fault.
While most jurisdictions (including all U.S. jurisdictions) have some form of no fault divorce, some jurisdictions still have fault based divorce, and if the other spouse is without fault, a divorce may not be available.
- Marriage would render conduct of a party criminal.
In additional to laws criminalizing incest, there are also laws that criminalize adultery (including those of the U.S. military), laws that criminalize bigamy and other forms of polygamy, laws that criminalize marrying a minor, and laws that criminalize marriages to persons in positions of trust. An annulment could be a defense to these crimes.
- Marriage could expose someone to tort liability.
Marriage to someone who is divorcing sometimes gives rise to heart balm tort liability which still exists in a few U.S. states, as the person who destroyed someone else's marriage that ended in divorce. Annulment could limit or eliminate that liability in some cases.
Also sometimes a spouse is liable for the other spouse's debts (under the necessities doctrine, for example), and that liability could attach during a brief marriage, but not during a putative marriage which is annulled.
- To prevent irrevocable loss of an occupation.
Some forms of employment (e.g. as Catholic priests and members of holy orders, and as Orthodox Christian bishops, or historically as one of the Vestal Virgins in pagan Rome) require that one be unmarried at all times. Annulment could prevent the permanent loss of eligibility to serve in such a profession.
- To prevent a loss of government benefits.
Sometimes a person is qualified for government benefits (such as Medicaid or Social Security survivor's benefits or Section 8 housing benefits) if unmarried, but not if married to a moderately affluent spouse. Marriage could terminate these benefits and it could take a considerable amount of time to regain them following a divorce. Annulment would prevent these benefits from being lost in the first place.
- Annulment could prevent someone from gaining a spouse's citizenship.
This is the flip side of the "fraud marriage" where someone improperly uses marriage to try to be a citizen. Maybe someone wasn't to not gain a spouse's citizenship.
Some countries grant citizenship to a spouse by operation of law upon marriage (e.g. France, at least historically). But, it could be that there are reasons that being a citizen of that country would be problematic (e.g. if the U.S. were at war with France, French citizens were being put in internment camps, and restoration of citizenship functions of the government have been suspended during the conflict for former French citizens). Annulment could prevent a person from acquiring citizenship by operation of law.
This could also affect the citizenship of their children.
- Other process considerations.
A divorce typically requires that the parties make full and fair financial disclosures to each other before a separation agreement or divorce decree can be entered. An annulment does not.
Comprehensive financial disclosures, particularly in the case of a very affluent spouse or spouses, can be extremely time consuming, cumbersome, and expensive, and may also require disclosure of secrets that one of the spouse would rather keep secret from their putative spouse and the court.
- To retain autonomy.
In some countries historically, and in some Islamic countries now (e.g. Saudi Arabia), the rights of married women are very different than the rights of unmarried women, with married women surrendering considerable autonomy to their spouse (e.g. the right to choose a place of domicile or to live separately from a spouse, or to write a will leaving everything to someone other than a spouse at death). Lack of autonomy at a key moment could invalidate an agreement the putatively married spouse entered into. Annulment would validate the agreement or decision.