According to Catholicism, why do we need a resurrection if we have an immortal soul? Here's this other question that asks the question "According to Roman Catholicism, how old will our resurrection bodies be?"

The answers to the question talk along the line of that a persons physical body is resurrected. One of the answers includes this segment from the Catechism of the Catholic Church


  The "resurrection of the flesh" (the literal formulation of the
  Apostles' Creed) means not only that the immortal soul will live on
  after death, but that even our "mortal body" will come to life
  again.


(emphasis added by me)

My understanding about Catholic beliefs, and about Christian beliefs in general, is that inside ourselves we have an immortal soul that continues living after the body is dead. Answers that talk about the Catholic view of this can be found for example here and here.

Question:

According to Catholicism, what do we need a resurrection for since we have an immortal soul that survives the death of the body?
Although I am not a Catholic, I feel confident that I can answer this, as the answer is shared by all Chalcedonian Christians.

This question really gets to the heart of what it means to be a human. And the best way to answer that is to look to the incarnation of Christ.

In the incarnation the eternal person of God the Son was united to a finite human nature. Chalcedonian Christians believe that the incarnation was not just God the Son talking on a human body, but a complete human nature: a human soul, a human mind, a human will, human emotions and desires. Just as a human body has many organs but none of those organs are enough to be called a human by themselves, so too a human person has physical and non-physical parts, which by themselves are not enough to be considered human by themselves. In the early church Apollinaris argued that Jesus had just his single divine mind and took on a human body. This was declared to be heretical by the First Council of Constantinople, as it meant that Jesus was not fully human.

Many Christians today fall into the same trap. I've heard Christians say that we are a soul who has a body. This is a departure from orthodox Christianity which says that the human nature is a complex union of body and soul (a complex union in the sense that it is one thing but yet has distinct parts or aspects.) Instead we should say that human beings are body-soul unions. While the human soul and body may be temporarily separated from each other, that is an unnatural state for a human to be in. Just as Jesus Christ forever remains incarnate in the flesh, so too will the souls of all humans be reunited to flesh in the resurrection.