Tell the PI that standard deviations are for data. It is associated to the mean in the sense that a standard deviation provides a measure of how close some random future observation will be to the mean estimate.
In a similar way, you can think of a standard error as a way to think about how widely the parameter estimates will be expected to vary if you collect new data. A SE gives you a sense for how accurate your parameter estimate is.
If that is too abstract, you can also use the more familiar notion of a confidence interval. A confidence interval says that, given the data, the true parameter is probably within a certain interval (with some confidence). Standard errors are often used to construct confidence intervals. A big standard error leads to a wide CI; a small SE leads to a small CI.
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