What is the semantic difference between everybody and anybody in `doing` context?

Question

Please explain what should I choose for what context in the following examples:

it lets everybody do whatever they want
it lets anybody do whatever they want

What is the semantic difference?

Answer 1

The choice depends on whether you are targeting the statement at individuals or at the group. So you might say:

Anybody who needs to use the toilet should go before the show.

Here you are thinking of individual actions and any is the better fit.

On the other hand, you might say:

Everybody who bought a ticket for the show will get a refund.

Here you are thinking of the people as a group, of all those who bought tickets, so every is the better fit.

What dictates your choice is the context. In many contexts, either word will fit. This is true of your examples. The choice would depend on the context, what you are referring to and the make-up of the group concerned.