Why does Amos specifically mention Bethel (verses 5-6) other than that it was where the Israelites were holding feasts? Why did they choose Bethel as a feast site? Bethel played an important role in Israel's history. Twice Jacob, one of the fathers of Israel, has important events happen to him there.
Genesis 28:11-22 records the first occasion Jacob has an encounter with God at Bethel, though it was not called Bethel then. It received its name—"House of God"—from God revealing Himself to Jacob there, and Jacob believing that He lived there. On this occasion, the patriarch arrives as a homeless wanderer, a man on the run from the murderous intents of his brother Esau. He is a man with a past, having just deceived his father and brother out of the blessing. Nevertheless, God reveals Himself to him there, and the transformation of Jacob begins. He leaves Bethel as a man with a future.
The second time he encounters God at Bethel (Genesis 35:1-4, 7, 9-15), he arrives after departing from his father-in-law, Laban, and having reconciled with Esau. He is a far better man than the first time, but he is not yet complete. However, he arrives as "Jacob" and departs as "Israel." The new name is assurance of the reality that he is a new man, that a transformation is taking place. In the Israelite mind, Bethel thus became associated as a place of renewal, of reorientation, of transformation by God.
Even as verses 1-3 of Amos 5 are a dirge, verses 8-9 are in the form of a hymn praising the true God, the transforming God. When God is at work, things change for the better; He is the God who makes a difference.
With this background, we can understand why Amos 5 calls attention to Bethel. God is asking, "Why aren't you Israelites being transformed in the conduct of your life when you keep the feasts?" He is saying, "You indeed go to Bethel for the feast, but no transformation of your conduct and attitude occurs. Are you going there to seek Me?"
One of the primary proofs that God is making a difference in a person's life occurs when one who was formerly hostile to God and His law begins to love God and His law. He shows his new love by obeying God and His law in his life in areas like those mentioned in verses 10-12.
Yet, the Israelites attended the feasts in Bethel and returned home with their lives still ungoverned by God's truth. When Jacob met God, his life began changing immediately, as his vow to tithe in Genesis 28:22 shows. Faith immediately became part of the conduct of his life. The lives of those in Amos' day should also have changed according to the dictates, principles, and examples of God's Word. They should have left Bethel singing and exemplifying, "Oh, how I love Your law! It is my meditation all the day" (Psalm 119:97).
It seems that these people turned the feast in Bethel into nothing more than a vacation. Thus, Amos admonishes, "Do not seek Bethel! Seek the Lord and live!" Ultimately, the Bethel approach signifies death, not life.