Well, starting with the earlier tradition, the Eastern sign of the cross allows you to make a hand sign that corresponds to an I, an X, and a C. It gives you a connection to a particular Christian lineage from a particular part of the world. It indicates that this is where you came from, and this is what they’ve given to you.
If you’re in the West, you probably follow a less ancient tradition with five fingers and a side-to-side motion that’s opposite of the more ancient tradition. I could ask why you don’t do the more ancient tradition, but the answer’s pretty obvious: You don’t have a connection to the more ancient Christian lineage from that particular part of the world, that isn’t where you came from, and that isn’t the particular tradition that was given to you.
For many non-Catholics, we feel like our strongest connection to Christianity is in America rather than somewhere in Europe or Asia. Consequently, we don’t have a strong connection to either the more ancient or less ancient traditions that began there. Some of the mainline Protestants that broke more directly from Rome (more or less) took certain traditions with them, but for the Western non-Catholic who didn’t break directly from Rome, we don’t really feel like we’re any more connected to the Western tradition than to the Eastern one, and in any case, it doesn’t seem like anyone intended to pass it on to us.
If we had such a connection or if one of those traditions had been passed on to us, it would make more sense for us to do it. I’m sure there would be more of a payoff, too, since we would regularly recognize our connection to a more or less ancient tradition. But for many of us, we don’t feel like we really have that connection, and if we did this, we’d be misappropriating something that wasn’t given to us in the first place. If we had the connection and if this had been given to us, there would be more of a payoff. But since there is no connection at all for some of us and it hasn’t really been given to us, I think there’s a payoff for you guys but not really any for us.
All of that’s totally fine, you know- I’m not complaining about how any of it is or what anyone’s doing. I think pretty much everyone is doing (or not doing) the things that make the most sense for them, and for people from different parts of the world and different liturgical backgrounds, it’s going to look different from person to person.