The difference between purity and impurity has to do with order and disorder. By trying to remove those things which are impure, an effort is being made to remove those things which are disorderly and destructive and instead focus on what brings us order and life. God requires the maintenance of purity because His ultimate goal is always to bring us into communion with Himself. However, we cannot be brought into communion with the One who is all good if there are parts of ourselves or our lives that are impure and disorderly. This idea of requiring the maintenance of purity, which leads to the maintenance of order, recalls the story of Creation, where God created and ordered things and then handed on the task of ordering to humans. If we are now responsible for the task of ordering creation, it would make sense that God would require the maintenance of purity and order in our own lives. How can we be expected to create order in Creation when there is no order to things in our own life? Therefore, God gives the Israelites the laws to help them maintain purity so that they might be able to be closer to God and better able to experience order.
The logic behind the food laws is that our bodies are a reflection of our spiritual life. Because of this, God required that everything the Israelites consumed was pure. By doing this, He helped them to purify their spiritual life so that they might be able to enter into communion with God. By following the food laws and purifying themselves, not only do they purify their spiritual lives, but they bring order and purity to their lives on Earthy as well.
Answers to Daily Questions (Catherine) 
To your point that “our bodies are a reflection of our spiritual lives,” Jesus Christ himself was the paradigm spiritual figure which we should all try to live like in regard to faith, and he stated numerous times in the New Testament that his body was his “temple.” Surely there is a correlation.
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I think it’s interesting how you compared our bodies to a temple, with only allowing that which is righteous to enter. It was interesting to see what was deemed as acceptable, with the order of creation in Genesis serving as the general guideline, showing the interconnectedness of the chapters in the Bible.
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I also agree that we ourselves must be in our most pure state to live out the message of Christ and to receive his blessings fully. Just as the Israelites were called to do so, we are also called to experience disorder in its fullest form. The food laws, although strange, bring order into a new form of our everyday lives and promote obedience.
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I like your approach to the question. Another point you might want to consider is mentioning how we were also made in the image of God, and hence order and purity are in our nature as a fundamental need.
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