According to my Bible, pigs were a common animal used by pagans for religious sacrifice (which means they were probably raised and eaten as well). If the Israelites couldn't eat pigs or use them for sacrifice, they had no use for them. That meant that there was one less link between God's people and the Pagans surrounding them.
God wanted His people to be holy (set a part, different, unique) because He is holy. He knew that mixing with the Pagans would loosen their grip on who they were as God's people because of the compromises they would make over time. It seems like many of God's rules could have served a double purpose by keeping the Israelites away from those who could and would defile them (not associating with certain animals limited reasons for social or business interaction with pagan communities).
This is yet another change that Jesus brought about with the cross. When Jesus was on earth He explained that food doesn't go through our heart, just our stomach, so eating certain foods won't defile us but acting in certain ways will (Mark 7:14-19). This is why I think that the food restrictions were put in place more for spiritual health than physical. When we live with Jesus and have the Holy Spirit inside of us,God wants us to go out into the non-christian world and declare His name. The difference between then and now is, simply put, Jesus. If we love Jesus, He lives inside of us which makes it quite a bit harder to be defiled by the outside world. Also, we can go preach to people because we actually have hope and salvation to share with them (an eternal purpose for association!)
Side Note: My study Bible also pointed out that God not only says not to eat them but even touching them will render you unclean. Direct Quote: "He wanted the people to be totally seperated from those things He had forbidden. So often we flirt with temptation, rationalizing that at least we are technically keeping the commandment not to commit the sin. But God wants us to separate ourselves completely from all sin and tempting situations. Perhaps this passage has made you aware of areas of your life where you have "technical" innocence but in which you have actually been involved in sin. It is time to cross back over the line and stay there." That note really hit home for me because I tend to do that a lot. You know, thinking to yourself, "well, mom didn't say I couldn't be reading" but knowing that she did say to do you homework. So yeah, this is definitely something that I need to work on! And if you do too, I hope that you found this as encouraging and enlightening as I did! :)
Expansion on the Chronological Life Application Study Bible