Swallows symbolized the incarnation of Christ.
Swallows make their nests from mud and, in what passed for science back-in-the-day, mud "made" swallows. Jesus, as the 'new' Adam, was also made of clay.
Swallows make their nests in barns. Christ was born in a barn.
Swallows are almost angelic in their flight. Christ seemed to almost be an angel. OK, I know that is bad theology, but work with me here.
Swallows disappear and yet we know they will be back. Early Christians believed that Christ's second coming was imminent. Even today, Christians believe Christ will come back.
Symbolism was serious business
Today we look at symbolism as fun or intellectually stimulating.
Back-in-the-day it was a capital offense to be convicted of following Christ.
Use of symbolism allowed early Christians to speak in "code" and still transmit the oral history back when "Letters" were rare because they were hand copied and even if you had one few people could read.