You might be thinking, but the New Testament does away with dietary laws! While it might seem so in a cursory glance, that is not actually the case. As far as eating blood is concerned, Genesis 9:4 is very clear that this is a universal law, applicable before Israel existed and as soon as God allowed meat eating. This is consistently recognized multiple times throughout the Old Testament, as well as in Acts 15 for what is still applicable to Gentiles. Acts 15 lists four prohibitions that were likely not clear to the Gentiles joining the church (no eating of blood, no eating of strangled things, no eating of food sacrificed to idols, no sexual immorality), whereas things like clean and unclean meats were already very clear to them, as we will see next.
In all the passages related to unclean meat in the New Testament, Paul and Jesus use the word common, not unclean. This indicates that they were addressing the concept of defilement by association, which arose after the exile when the Jews tried to avoid breaking the clean/unclean law (which they had broken before exile, and was one of the reasons they went into exile), by also not eating or touching anything that had touched something that was unclean. Jesus and Paul note that this defilement by association was not biblical, but that the clean/unclean distinction remained. You can see this clearly in the English in Acts 10:14 (Peter notes that he has not eaten anything “common” or “unclean”), and in the Greek in Romans 14:14 and Mark 7:17–23. In all these New Testament passages, God is referring to things called “common” (defilement by association) and pointing out that they should actually be acceptable, unlike what the Jews had added to the law. But the clean/unclean distinction is still valid.
As far as why certain animals are unclean and others are not, the Bible never gives us clarity. Many hypotheses have been put forward, but none of them fit all of the animals, although may be applicable for some. Perhaps this is similar to the Sabbath, in that God never gives a reason why He picked the seventh day, but He is calling us to be holy, and out of gratitude for His salvation, we delight in following His Word.
However, other laws in Deuteronomy 14 are not so clear as to what they mean, like the enigmatic reference to not boiling a kid in its mother’s milk. Out of this comes the Kashrut law regarding not eating meat and milk together (also referencing Exod. 23:19). While Kashrut could certainly be implied from this law, it seems likely that there was some additional situation that Moses is referring to, which has been lost today.