If you are arguing that asylum seekers should have the right to just go to any country of their choice where they have relatives and claim asylum there, then you are saying that they should have additional rights that no-one else has, and which are clearly not necessary in order to give them asylum/safety. I think that would require some justification.
But
claim does not equal
granted. I'm not sure why it's so objectionable that they should be able to seek to claim asylum somewhere that they think is best for them to do so for whatever combination of reasons. If whilst assessing their claim it turns out that they're, in fact, not genuine and have just tried to basically jump the queue then deport them ASAP (allowing for any appeals). Also we should surely want asylum seekers to spread out a bit. It seems extremely unworkable for the neighbouring countries to whatever unstable country is collapsing this week (seemingly it's Sudan's turn today) to have to deal with all the refugees from that place just because they have the, er, misfortune (I guess it's a misfortune in this case being a safe country?

) of being the closest safe country. Of course, they do tend to take the lion's share as, funnily enough, most asylum seekers actually want to go home once it's safe to do so therefore staying close makes sense. Ukraine being a good current example of that effect of course.
Equally asylum seekers are, of course, disadvantaged compared to someone who might want to move to Outer-Faraway-Land in a number of different ways. Because it's easier to type than Outer-Faraway-Land

)) I'm going to go with Canada instead. But if I wanted to move, as an economic migrant, from the UK to Canada because I decide I'll have better prospects there then, by virtue of living in a safe and stable country, I can take my time to gather the various documents that I will need, to review the criteria to apply for whatever visa I need, take advice on what I need to do, prepare my application, go to the embassy several hours away to undergo whatever interviews or other hoops might be required before finally getting my visa. The likelihood that an asylum seeker is going to be able to do that is negligible. Just because they've had to flee why should they be confined to the first safe country? Just because they couldn't sit tight and jump through all the required hoops?
We're lucky that we don't have to worry about fleeing the UK but if we lived in an alternate universe where Corbyn had won in 2019 and brought about a second Bolshevik Revolution and bands of nouveau-Cheka were now roaming the streets purging counter revolutionaries (I think that's what the Daily Mail said would happen?

) should we only be able to flee to Ireland, France and Belgium? They're all the closest safe countries. But why couldn't I seek asylum in Germany or Austria where I at least speak a few words of the language (C at GCSE German and a two year streak on Duolingo!)? Or Australia where I have relatives plus the benefits of a shared language and culture?