Tuning Isn't Hard, It's Just Imperfect
Your guitar isn't broken, and your ears are fine too!
Anyone who has done any woodworking project of any complexity, like building a birdhouse, or a bookshelf, or even put in wood flooring, knows that wood is not perfect. It warps, it gives, it twists, and it expands & contracts. When tuning a guitar, I always have a little voice in my head reminding me “remember, it’s just wood”, and that helps me muster the patience to get through the tuning process.
No matter how well-made a guitar is, no matter who built it, no matter how long it has had to “season”, no matter how much that guitar cost, it will never be “perfectly in tune”. Depending on the method you use to tune the guitar, it might sound perfect for some chords, and obviously out of tune for another. Or two strings that are obviously in tune with each other sound out of tune with each other when you play a certain chord.
This is true even if you’ve just had a proper setup, your strings are properly stretched, and the guitar is in perfect working order. The problem you’re running into is that you have to “remember, it’s just wood”.
When you tune a guitar to standard pitch, using the old Mel Bay method where you put your finger on the 5th fret of the low E and compare it to the open A, and so on, you do so by pressing down a fret, and comparing it to an open string that has no frets pressed down, and then you continue that pattern down the strings to get them all “in tune”. If that’s how you tune, then you’ve no doubt noticed that playing a full, open G chord right after is often clearly not in tune.
When I was a kid, I would tune using the Mel Bay method, play a G chord, and immediately start making up stuff to get the guitar in tune, like playing the open G string with the 3rd fret on the high E. Or focusing on the open D and open G strings together. I’d do this for a couple of minutes, and eventually I felt like the guitar was “in tune”. Then I’d play a song that had a C chord in it and feel like I was back to square 1 and had to tune again!
At different times, I thought I was crazy, I thought “this guitar sucks, I need a more expensive one”, I thought “I just had a setup, I’ll never go back to that guy again!”, and more. This was at a point in my life where I just didn’t realize how important it was to “remember, it’s just wood”.
As I got out & played with more experienced players, I always watched them closely to see what I could learn from them. Surprisingly, what I learned was that they seemed to tune constantly between songs. They had better guitars than I did, and I had just listened to their last song and they were sounded perfectly in tune to me. I later learned that they were tuning between songs because the next song has a lot of open G, and the last song had a lot of open E, and on their guitar if one of those sounds perfect the other doesn’t - you had to tune just slightly differently.
Today, I happened across a video of none other than Vince Gill showing how he tunes a guitar by ear. He goes through & tunes a couple of different acoustic guitars, while casually discussing the process with “Uncle Larry”, who is also someone worth learning from. Like his music or not, it would be very, very hard to conceive of someone more qualified than Vince Gill to learn about this from. In the video, Vince says, explicitly: “I’ve always though it was a pretty imperfect science”.
One person you might conceive of as being as good to talk to about this, though, is James Taylor. He made a video specifically to teach you how he tunes his guitars, and it is far more analytical and scientific, and I can’t imagine doing this in any kind of live setting, but the video is over here, and it’s 100% worth watching (in fact, both Uncle Larry and Vince Gill mention having seen the James Taylor video though, like me, neither has ever tried his method). Watching both videos completely will likely fill in some gaps.