Hello! I'm an EdgeR user, and I would like to know how this program calculates the log2FC for 2 sets of samples (treated vs. control).

For one gene, I would calculate its log2FC as the logarithm(2) of the ratio between the mean of normalized counts in treated samples and the mean of normalized counts in control samples.

But, if I do this operation manually, the result is not the same as the EdgeR one. Any reason behind this difference?

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Now, as to your question, you cannot directly compute the log fold change, as there is no closed form of the coefficients for a generalized linear model. The log fold change is computed internally, using an iterative function, and helpfully extracted for you. So the reason there is a difference is that what you are calculating isn't how the log fold change is calculated.