why do asylum seekers choose to arrive by boat as opposed to applying for a refugee status with UNHCR?

If you're talking about the US, relatively few come here by boat. however, it's possible to apply for refugee status through UNHCR, but the process can take several years or more and you may never be resettled in a third country. during that time, you'll probably be living in a refugee camp, which is usually unpleasant at best, and sometimes dangerous, depending on where you are. and you don't usually have a choice on where you'll be resettled if it does happen.

you can only apply for asylum if you're already in that country. so, during that time, you can live a relatively normal life in the country of your choice.and, as noted, the process can go on for a few years, depending on how willing you are to appeal every decision. it becomes increasingly expensive though, unless someone is representing you for free, which does happen from time to time,, but usually only on very prominent cases.

Because they can stay for a while, and stretch out appeals for years if they just show up. They will have hearings with a judge, and get tons of appeals. They are where they want to be for the duration.

If the apply to the UNHRC, they get turned down by the UN right away, and they don't get years of living it up on the taxpayers' dime.

As far as I'm aware, you have to actually be inside the country to apply for asylum-seeker status.