For me, BC, fingernail length varies, depending on what phase of practice I'm in. When I'm learning new pieces, I like longer nails to help find the string. As I get closer to the concert, I like shorter nails, for brilliant sound. These are the trade-offs: long nails to help find the string, and short nails for brilliant sound.
When I am in the acquisition phase, I found that short nails produced a stilted sound, too short and controlled. I had to stab the string to find it. It wasn't good. You may want this sound in certain spots, but you don't necessarily want it all the time.
When the nails are long, I found I was getting noise as I pushed across the string, a "wiping" sound. When I played flute, I liked a softer attack on the note, but on guitar the softer attack produced a 'wiping' sound which my teacher could not stand and he told me so, in no uncertain terms. Flute good, guitar bad. If your teacher thinks you would like shorter nails, you might want to listen to your sound in terms of the quality of the attack. Maybe he's trying to tell you something.
In guitar, there is only one thing, the gesture, the attack. We only get the attack -- sustain and decay are up to the guitar. And we get the closure of the sound, if necessary, but that is another topic.
While the guitar has "an unlimited tonal palate" [Segovia], and "unlimited consonant sounds" [Collins] you would prefer not to take advantage of your audience's patience by wiping the string every time, playing with only one consonant sound.
I would look at the "push across the string", then, and see if the nail is "wiping", rather than crossing the string on one point, and clean that up. You would like to have a variety of sounds available to you, not just a "th" sound.
The other problem may be "catching". I like to create a striking surface on the nail by placing my sapphire board under the nail and filing a flat striking surface.
Flat striking surface with sapphire board
The shape of the striking surface will vary according to the curve of the nail. I think we have all tried different nail shapes and that is how I get mine. Then I file the nail to a symmetrical shape. Mine is curved but others have a flat striking surface with the nail filed at a distinct angle.
Here is a drawing that shows the issue about trying to describe "nail shape":
Without seeing the actual curve of the nail, from the top, the drawing is meaningless. The two nail shapes may create the same striking surface for each of the two individuals. We will never know.
I would keep the side off, though, that soft spot where the nail tends to catch and break, when I'm putting on my socks in the morning, before my eyes have opened.
So, I would look closer to see what your teacher is saying, some things things are lost in translation between two individuals. You could become an active observer, check a couple more angles.
Maybe your teacher is right. Try it shorter, just a little at a time. They grow back.
My $000,000,000.02 worth.
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Kevin Collins, Amherst, Mass, USA All rights reserved.