There's no valid argument for that. Incorrect arguments are either just refusals to accept some aspect of SR, or incorrect calculations that if they had been correct would have proved that SR is inconsistent.
Are you interested in physics, history, or sociology? Historically, there was surely some doubt about SR ca. 1905-1915. The Nazis carried out a campaign of ridicule against "Jewish" science, including relativity. There are kooks today who insist that relativity is all wrong. If you're talking about physics as opposed to sociology or history, then there is no serious argument to be made today that Galilean relativity is more valid than SR.
Sadly, there are a lot of websites, papers and other stuff published that attack relativity. Most of these always refer to it as 'Einstein's' relativity, which makes me wonder if there isn't an element of racism motivating the ( crackpot) 'refutations'.
Racism might play a part, but I think it is a small part. The racist idiots tend to use the argument that relativity isn't Einstein's idea, and that none of his 1905 papers are.
(Irrational) reasons to argue against relativity:
Moral relativism is absolutely wrong. Therefore any form of relativism is wrong. Therefore relativity is wrong.
"If I can show that Einstein was wrong then I must be smarter than Einstein."
Making ridiculous claims makes some people think they are edgy.
Lawyer training? I swear that the re-vamped flat earth society web page was created just for lawyers-in-training. I can just see the class assignment: "Defend the notion that the Earth is flat. Here is the web site where you can do that: ..." Perhaps some of them have edged over to refuting relativity.