Why is the NT so anti-rich?

In Luke 6:24, Jesus bluntly and concisely states the NT perspective on the rich: "Woe to the rich."
James 2:6 (RSV) explains why: It's because the rich oppress the poor.  In much more detail,
James 5:1-6 explains what the "arrogant rich" (The Message) are doing.  Often the oppressive rich are also the religious rich and the ethnocentric rich in the NT.

In Luke 19:47, Jesus described the temple as "a den of robbers".  The temple was by far the most important social institution in Palestine.

Jesus described the Pharisees as "full of greed", Luke 11:39, and as "lovers of money", 16:14.  As a result greed crowded out "justice and the love of God", Luke 11:42.

As a result of the religious rich and the oppressive rich dominating both the religious and economic institutions of Palestine, Jesus called for them to repent before they could enter the kingdom of God.
See Mark 1:15, Matthew 3:1, Matthew 4:17.  In Luke 4:18, there is a further explanation of why repentance was an absolute necessity.  Jesus says the kingdom of God is for the poor and part of a kingdom ministry is to release the oppressed.  Only when the rich repent and restitute can the oppressed be released.

In Luke 3:10-14, John the Baptist elaborates on the type of repentance needed; note that all of John's illustrations of repentance are economic in nature.  Examples of repentance in the NT are few and far in-between; but an outstanding example is found in the story of the tax collector Zacchaeus.  As proof of his repentance, Zacchaeus engages in restitution returning four fold what he had stolen.  The other remarkable account of repentance and restitution is found in the book of Acts 4:32-33.  Here the Spirit-filled rich sell surplus houses and lands and bring that money to the church and then the church distributes this money to the poor.  So Acts states specifically there were no poor or needy among them.  This is the radical nature of the kingdom of God when its incarnated here on earth by the church.