The paradox take into account the vast distance between stars.

The idea is that in the billion of year of the universe, even when going very slow, even if it take 1000+ year to get to the next star with a generational ship, and then another 1000 year to build a society on that planet before launching the next ship, the univers is so old, that if there was an intelligent alien, it must already have colonized ALL the milky way. ALL of it, every star, and there are a lot. As big is the space, the age of the universe is far far bigger.

Another counter argument, beside the usual (earth is a zoo monitored by hidden alien; life is super rare; intelligence is super rare and we are the first; there is a great filter that kill any intelligent life during their time, alien dont care to expand as in the article..) ; so another one is from kurzgesagt :

It state that life appears so fast on earth, and grew so fast, that it must have been already a long way into its evolution. The first microbe was already super complex. So, may be it took the billions of years of the universe to get to that first microbe. So we are amongst the first intelligent life that can exist, because life took so long to get the first microbe. And only now can start the colonization for every intelligent species