On a practical level, the risk of dropping blood or the body should be quite apparent. When the priest intincts he can be holding the body over the chalice the entire time and, ideally, the chalice over a veil two servers are holding (I don’t even like it - I’ve seen some Syriac Orthodox churches and Byzantines do this - where the communicant holds the veil; if they’re careless passing it around, anything they catch falls on the floor anyway). Additionally, if someone is careless they dip so far they dip their fingers into the chalice, which is a sanitation issue if the whole church is dipping their hands (where who knows where they’ve all been) into the chalice.
On a theological level, at least in the West Syriac Churches, the body is called the gmurto (coal). Isaiah certainly didn’t grab the coal from the altar in Isaiah himself. The analogy is meant to illustrate it is of heavenly origin being dispensed to humans and it should be treated with the upmost care and reverence, handled by holy hands set aside to handle holy things. There was an almost universal development, save the East Syriac Churches, away from the individual communicants handling the body and blood themselves for whatever reason (I’m inclined to think the practical reasons might be the primary cause of that though).
I don’t quite understand why Latin are so vehemently against self-intinction, though, aside from their own custom and they must assume you’re not Catholic if you self-intinct since they generally associate it with Protestants. They already handle the body with their hands so I don’t see what theological argument that could make against it. Though if I was in a Latin church I would follow their ritual, just like if I was in an East Syriac church.
