During the birth of Jesus, if the three Wise Men had to leave the star aside, which was showing them the right direction, and ask Herod who angrily killed all innocent babies 2 years old and below, why were they called "Wise Men"?

In the Greek, the word for wise men is μάγος or Magi. The term originally referred to the great scholars among the Medes and Persians who counseled the king and who studied astrology, medicine, astronomy and natural science. 

At the time of Jesus’ birth, God arranged an astrological sign to announce this wonderful event. The Magi, or wise men of the East, saw the sign and understood it. Reverently, they packed gifts for a king and then followed the guiding star from their Eastern land, possibly Persia. The Bible does not tell us how the star led the Magi, but apparently its leading discontinued when they reached Judea. 

Naturally they went to the palace of King Herod inquiring for “him that is born King of the Jews.” They would assume the king of the land would be well aware of this blessed event and would be in joyful anticipation of the baby king. However, “when Herod the king heard this, he was troubled…and…gathered all the chief priests and scribes of the people together, he inquired of them where the Christ was to be born.” Matthew 2:3,4. 

Herod’s counselors shared the prophecy that the baby would be born in Bethlehem (Micah 5:2, Matthew 2:6). Herod then secretly plotted the baby’s death. Evilly, he pretended he wanted to worship the new king, and he sent the Magi to Bethlehem to find the baby. 

Matthew 2:9,10 continues to tell the story: “When they heard the king, they departed; and behold, the star which they had seen in the East went before them, till it came and stood over where the young Child was. When they saw the star, they rejoiced with exceedingly great joy.” So, apparently the star reappeared and led the Magi to baby Jesus.

The Magi did not know Herod would try to kill the new born king, but God gave them a dream to warn them not to return to Herod. “Then, being divinely warned in a dream that they should not return to Herod, they departed for their own country another way.” Matthew 2:12.

Thus, these men were wise because they studied the stars, correctly understood their meaning, journeyed to find Jesus, blessed the baby king with gifts, and then obeyed the dream and did not return to see Herod. No other men on earth had the wisdom nor faith to journey to find the new baby king.