Here is another explanation for Latin rite Catholics crossing themselves from left to right:
However there can be little doubt that long before the close of the
Middle Ages the large sign of the cross was more commonly made in the West with the open hand and that the bar of the cross was traced from left to right. In the “Myroure of our Ladye” (p. 80) the Bridgettine Nuns of Sion have a mystical reason given to them for the practice: “And then ye bless you with the sygne of the holy crosse, to chase away the fiend with all his deceytes. For, as
Chrysostome sayth, wherever the fiends see the signe of the crosse, they flye away, dreading it as a staffe that they are beaten withall. **And in thys blessinge ye beginne with youre hande at the hedde downwarde, and then to the lefte side and byleve that
our Lord Jesu Christe came down from the head, that is from the Father into erthe by his holy Incarnation, and from the erthe into the left syde, that is
hell, by his bitter Passion, and from thence into his Father’s righte syde by his glorious
Ascension”. **
Here’s the link it’s from:
newadvent.org/cathen/13785a.htm