The way they arrived in Australia. That they attempted to enter Australia illegally by boat. And that doesn't apply to the US because these people have never attempted to enter the US.
I do have a few minutes now to do the copy and pasting, so here is the explanation of the policy. I'm not saying you have to agree with it, but it can at least be explained.
If you get on a boat without a visa, you will not end up in Australia.
Any vessel attempting to illegally enter Australia will be intercepted and safely removed beyond Australian waters.
The rules apply to everyone; families, children, unaccompanied children, educated and skilled.
No matter who you are, or where you come from, you will not make Australia home.
Australia has an absolute policy that nobody who attempts to come to Australia unlawfully by boat will ever be admitted to Australia. There are no exceptions.
The intent behind the policy is twofold - firstly to uphold the basic principle that we decide who comes here to live. Secondly, it's humanitarian - when we have not had this policy in place, many people have died trying to get here - drowning in the ocean between Indonesia and Australia as the small boats they used were not seaworthy enough to make such a journey. The policy that these people, no matter what their status, will never get into Australia, is the only thing that has proven to successfully deter these people from risking their lives. Unfortunately, the previous Labor government softened the policy for a few years, leading to a renewed influx, which is why we have people on Manus and Nauru now. Reintroducing the policy stopped the boats again, but we still have the people who came under Labor to deal with.
Australia does take refugees - but we take them out of camps overseas after they've applied for asylum and been processed, or in some cases if they enter Australia on a legal visa of some sort, and then claim asylum and are found to have a genuine case.
But you cannot attempt to come here illegally, and ever hope to live here. If you're a genuine refugee - do it legally, do it properly. That's the message.
Australia attempts to intercept boats on their way here and when we succeed we turn the boats back if it is safe to do so. If it not safe, the people aboard are taken to an offshore camp (commonly either Nauru or Manus Island) for processing. If they are not assessed as a genuine refugee, they will be sent home where possible. If they are assessed as genuine, Australia will try to assist them to be resettled in a third country - but not in Australia. We'll help genuine refugees, but we will not change our policy that if you try to come here illegally by boat, you cannot enter Australia.
These people fall into that category. Australia has identified their case as genuine - but they tried to come here illegally. We can't send them home because they are in genuine danger. But they can't come here.
None of this means that the US should take these people. America is under no obligation to do so, or to help Australia find a place to send these people. But I think people need to understand the situation. These people are genuine refugees who have already been subjected to pretty considerable vetting to ensure they are genuine refugees and they are unlikely to be dangerous. Australia is not seeking to send dangerous people to the United States. It's not a hostile act.
President Trump has already said he intends to allow a certain number of genuine refugees to enter the United States each year, after extreme vetting to make sure they are not a threat to the United States. These people have already been through years of such vetting by Australia and been found to be clean. And the US is free to (and presumably will) vet them again. That's a large part of the reason why the deal may seem attractive enough to the US for the new administration to go through with it. You're not likely to get 'better' refugees from anywhere, and you're still taking thousands.
The only issue is that these people tried to get into Australia by boat without a visa, and Australia will not make an exception to our policy on that, no matter how worthy the person of help is in any other way.
Under international law a genuine refugee is able to apply for asylum in a safe country. They are not supposed to be able to cherry pick what country that is. And that is the difference. These people tried to cherry pick Australia. And that's why we won't take them here.