Fun fact: The Roman salute was pretty similar to the national socialist one.
That's not actually true, if you're referring to Ancient Rome.
There's a single painting from 1784 depicting Roman soldiers performing that salute, but that was entirely artistic license.
There's not a single piece of ancient literature or statuary or imagery that depicts Romans performing that salute.
The only ancient sources that do depict or describe such a salute/stance only express a similar gesture that was used for wildly different reasons.
It's just because the Italian Fascist movement adopted the salute, basing it on that 1784 painting and other modern depictions of the salute, and proclaiming it Roman.
And then it was adopted by Fascists worldwide, particularly those of national socialist Germany.