There is literally no such thing as "Intelligent Design."
It's an admitted PR ploy, an attempt to backdoor pure religious Creationism into public schools and to legitimize it as a "scientific" theory to the general public.
The ID movement was an utterly dishonest attempt to backdoor religion into science class, yes, and undermine trust in science in general. Saying that there is no such thing as Intelligent Design, however, is likely going a bit too far. Intelligent Design is a common feature of quite a few religions, after all, which is something, and there are a number of Christians who believe that intelligent design happened, but are deeply offended if you try to lump their beliefs in with what they consider the dishonesty of the ID movement. Alien creators are postulated by some as intelligent designers, too, which is also something. And, of course, we are surrounded by things that were intelligently designed by humans.
With that said... there really aren't any good arguments for humans or life in general being intelligently designed, that I've seen. Arguments from incredulity regarding the complexity of life and how unimaginable it is that it could have come to be without a designer and appeals to how obvious it is that there must have been such a designer have seemed to be the most common arguments that I've seen for it. More rarely, there were the arguments that tried to abuse concepts like "language" and "code" to
"prove" it. If my memory's not been dulled a bit by the many years since I was more actively investigating the topics, the most "solid" argument that I saw along those lines was a guy who was trying to make a case out of DNA (along with RNA and similar) being uniquely and dramatically more complex among chemical structures that were claimed to be natural, but par for the course for something that was designed, to make a case that it should be treated as intelligently designed. On the sillier front, of course, there were things like the banana argument, as was already pointed out, a person popping a cell in a water filled test tube and claiming that the fact that it wasn't going to spontaneously reform was proof of life being created by an intelligent designer rather than abiogenesis, the quote mining from Darwin's The Origin of Species (especially when the issue was addressed in the very next sentence), and so on.