Pretty much the only reason that a team wouldn't offer arbitration to a starter like Odorizzi is if they had an absolutely stacked rotation where there was a better option. His stats are unimpressive but nothing kills a season faster than having 2-3 revolving doors in the rotation.
I am not a huge Ordorizzi fan.
But he was 26th in the American league in innings, 20th in K's, 24th in ERA, and 49th in WAR (including relief pitchers)
in 2018 that that places him in a low end #2 or high end #3 role in the American league, I find it interesting on how Twins fans some how magically think the twins prospects are going to be anywhere close to as good as that, history shows that doesn't happen.
I also find it interesting with all the stats out there, no one wants to look one of the most important ones and that is the percentage of prospects that don't live up to the hype.