Imagine trying to gauge a player’s offensive value without using any stats. Do you think you’d remember all 600 plate appearances the guy had during the season? You probably wouldn’t. You might remember the big hits or the times he really screwed up and your opinion of the player would be biased based on a small sampling of what you could remember.
This is pretty much the same point I’m going to make with the state of fielding statistics. There is no way you remember every single play Teixeira or anyone else has made during the course of the entire season and you might only remember the big plays, or you might only remember the plays that killed your team. It’s also possible that Teixeira makes the easy plays look difficult and you’re just not realizing it. There’s really a number of areas where your memory of what Teixeira has actually done could fail you.One of the best explanations of why defensive stats are important that I've read - Fangraphs