Well being a man doesn't mean you can't be an asylum seeker. One of the reason more men go is because they often are subjected to more torture, they are often forced to be within the military, they can face worse consequences in countries like Sudan, or the DRC etc.
For example, in Eritrea, men are often subjected to indefinite national service. Those who try to evade conscription can face torture, imprisonment, or execution. Many Eritrean men flee for this reason.
In countries experiencing civil wars, like South Sudan, young men are especially vulnerable to being forcibly recruited into government or rebel forces. If they refuse, they may face violent reprisals.
Men in conflict zones are also victims of sexual violence, more than we expect. In the DRC, the UN has documented widespread cases of men and boys being raped in detention or conflict settings as a form of humiliation and control.
You also cannot claim asylum until you are on UK soil, unless you are coming from Ukraine and Hong Kong. That it is the only current programme which exists, and I'm happy about that but it means for anyone else from many countries in turmoil have to reach here before you can reach asylum seekers. There is UKRS which an existing scheme for vulnerable refugees. You have to be referred for resettlement by partners such as the UNHCR.
Also before Brexit we were part of the Dublin III Regulation in which the EU tried to determine which member state was responsible for examining an asylum claim. In practice states could return asylum seekers to the first “safe” EU country they entered - however since Brexit we can no longer do that. So that's another reason why we now have to take more asylum seekers.
Finally the reason why many asylum seekers lack passports or documents is because first many countries don't provide the documentation, if you are fleeing from a dictatorship or a violent regime you can't exactly go to the passport office and say can I have one before you try and escape.
If your facing, a girl facing FGM cannot ask the local authorities for a passport as the community is often complicit in the practice, making official documents impossible to access without flagging something.Or like in northern Mozambique last week when Al Shabbah forcibly displaced many from their homes and killed some people, children watching decapitation, displacing thousands, burning homes and committing atrocities. Families had no chance to retrieve personal documents before running for safety.
In northern Nigeria, Boko Haram raids on villages force mass displacement. When insurgents seize homes and property, residents not only lose shelter but also identity papers.
If you're escaping the sexual violence across Goma and the DRC, you are at risk of retribution from the military you cannot travel to your home (which many don't have any more), to get documents, you have to flee and do so as quickly as possible. Military forces, or militias often deliberately seize or destroy identity papers to control populations or prevent escape. For instance, Rohingya refugees in Myanmar were widely documented as having their papers confiscated, leaving them stateless, on purpose.