What does “show up fielders” mean in a baseball game?

To show someone up is defined as:

to do something that embarrasses someone or makes someone seem stupid

In baseball, if a fielder makes an error, or doesn't get to a ball they may have been able to get to, it's considered inappropriate for the pitcher to complain about it or otherwise make it clear the fielder screwed up. The assumption is that the fielder knows they screwed up, and the pitcher should not pile on; instead, they should keep doing their own job.

This isn't really any different from any other workplace, to be honest; it's inappropriate to point out others' mistakes in public in general.

The video, though, seems to imply something else - that pitchers should not "show up" the fielders by making better plays than them? That's not a real unwritten rule of baseball, and in fact pitchers who make great plays are celebrated (shameless plug for my favorite play all-time, seen in person:

). What is true is that pitchers shouldn't try to make a play on a high fly ball that another player can easily get to, but that's because they're not particularly skilled at catching fly balls, compared to the fielder who is (and for traffic control purposes - the SS or sometimes the 2B is in charge of pop flys in the middle of the infield, as they can see the whole field and are presumably the best fielder.)