When someone says “You’re just being modest!”, what do they mean?
Do they mean that your estimation of the relevant aspect of your person is off, lower than in reality, or at least lower than their estimation of the same? Or do they mean that your self-reported estimate is lower than what you really believe it is, which is to say you are lying?
I see no third possibility here. So why is modesty a desirable trait? It’s inaccurate (in their eyes) and/or a lie. If it’s inaccurate there are two possibilities: Your standards are too high or theirs are too low.
If you are striving to hold yourself to reasonably high standards and be as accurate and truthful as possible in your speech, it does not help to strive to be modest.
What it’s about is social grace. In a culture of modesty, accurate self-assessment is read as arrogance. In a culture of braggadocio, it’s read as modesty, often false. This is a game you can choose to play, or just be accurate and let the chips fall where they may. Depending on what’s on the line, the latter approach can be simple and appealing.