What's wrong with cooking a kid in its mother's milk?

In sensus plenior (a Christian hermeneutic in which Jesus is always the answer) dietary restrictions become easy to understand:

The reasoning for the answer will follow this outline with example to make the point:

   They are changed indicating that the underlying ante-type has been fulfilled.
   The dietary laws have no moral component literally, they are pictures that teach a moral concept.
   Mixing is a picture of the cross, the command not to mix indicates that only Jesus can reconcile Law and Grace.

God's morality does not change, so when a law is changed, it means it has no moral aspect to it.

"The law, having a shadow of the good things coming" Heb 10.1 tells us that the shadow of the law, not the law itself needs to be examined, mindful that the pashat never loses it's meaning. The practicing Jew during that time was bound to practice it, because they were called by God to be His witnesses. The prophets played the same role within Israel, and were often called to play out, prophecies.

Drash:

All of the laws which prohibit mixing are one picture which teaches that we are not to mix law and grace, flesh and spirit. God's nature is that He is both Holy and Love (law and grace). But in his revelation to man, we cannot understand either if they are mixed. If a judge gives mercy we say there is no justice. Mercy and justice were recombined in God's revelation of himself at the cross. Christ is the firmament between the waters. He is the evening and morning star between the Holiness of Day and the Grace of night. He is the God-Man who is Spirit and flesh.

The dietary law was changed to indicate that picture was fulfilled in Christ.

The lobster which is an abomination was not a moral abomination, it was a picture of those who snatch the believer (clean fish) from the water (word) and drag them to the earth (flesh). This is a picture of those who cause a little one to sin. The underlying meaning of the picture is an abomination. see Mt 18:6.

The clean animal ruminates on the word of God and it produces a separated walk (split hoof). The unclean animals (understood by SP as the Pharisees) have a 'holy' walk, but it is based in their own laws rather than those of God. The scribes meditated upon the word, but it produced no holiness. The pig is indiscriminate what it eats. The dog returns to it's vomit, consuming the old word that they rejected when they received the new word in repentance.

Concerning boiling a calf in it's mother's milk:

Milk is in the class of 'oils' representing 'spirit' and meat is flesh. The spirit is what gives life and is an aspect of Holiness, since all flesh dies but is not dead yet, it is under grace.

Boiling represents tribulation. So boiling a calf in it's mother's milk is a picture of Christ in tribulation reconciling Holiness and Love, law and grace. Only he can do that, so it is prohibited for us to do that.

It is repeated three times as a hint pointing toward it's fulfillment at the cross. (3 days in the grave). Hints are called Remez in Midrash and sensus plenior.

In the pashat (literal), prohibiting the action helped separate the Hebrews from the pagan practices of their neighbors.