I am an immortal and so are you; it's just that not everybody realizes this.
The Catechism of the Catholic Church (CCC) teaches that a person's soul is immortal, is created immediately by God, it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection.1
People get some crazy ideas about what we are and why we're here. PETA thinks we're all merely animals and therefore equivalent: bug=fish=dog=boy. Another old heresy comes from the Albigensians2 that holds only the soul is important and needs to be freed from the body.
Fact is, the body and soul are a unity3, profoundly linked.4 Death itself is only a temporary separation, not the end.
So how do we deal with all this? I'll leave it to you to figure out how to counter PETA - it seems a fairly shallow philosophy; as for Albigensians:
Two men considering a religious vocation were having a conversation. "What is similar about the Jesuit and Dominican Orders? " the one asked.
The second replied, "Well, they were both founded by Spaniards -- St. Dominic for the Dominicans, and St. Ignatius of Loyola for the Jesuits. They were also both founded to combat heresy -- the Dominicans to fight the Albigensians, and the Jesuits to fight the Protestants."
"What is different about the Jesuit and Dominican Orders?"
"Met any Albigensians lately?"
 Catechism of the Catholic Church (CCC), para. 366
 New Advent, Catholic Encyclopedia, http://www.newadvent.org/cathen/01267e.htm
 GS 14 § 1; cf. Dan 3:57-80.
 Catechism of the Catholic Church (CCC), para. 365