While the Bible does not state all of reasons God used to justify wanting to kill Moses, we can take what information is available and derive a fairly good explanation. Although it may seem outwardly there was nothing wrong, to God nothing is hidden!
The issue of punishing Moses by killing him surrounds circumcising one of his sons. Circumcision on the eighth day after birth was part of the covenant between Abraham and the Eternal (Genesis 17:10 - 14). This act eventually became part of the agreement between God and Israel. Every male child had to be circumcised or else 'that person shall be cut off from his people' (Genesis 17:14).
The Confrontation
The Bible states that the Lord, while Moses was in Midian, told him to go back to Egypt (Exodus 4:19). Something extraordinary took place, however, while he and his family travelled to the land of Pharaoh.
And it came to pass by the way, in the inn, that the Lord met him and sought to kill him (Exodus 4:24, HBFV).
Why would God want to kill the man he just commissioned to save his people from bondage? Zipporah's actions give us a clue.
And Zipporah took a sharp stone, and cut off the foreskin of her son, and threw it at his feet, and said, "Surely a bloody husband you are to me." So He let him go. Then she said, "You are a bloody husband," because of the circumcision (Exodus 4:25 - 26).
Moses had two sons named Gershom and Eliezer. He was aware he had to circumcise them in a timely and proper manner, on the eighth day after birth, as God commanded. He had previously carried out the ceremony for one of them (note that Zipporah only had to circumcise one of them to quell God’s wrath) but not for the other.
Possible Reasons
We can only speculate as to why the ceremony of circumcison was not performed. Perhaps He may have thought the act was not that important and therefore did not do it. He may have been squeamish about performing such a delicate but bloody act a second time after doing so once. He also could have easily justified to himself not carrying it out knowing his wife, a non-Israelite, would have been displeased with him performing it a second time.
What is clear from the Bible is that Zipporah understood the threat to her husband. She knew he would have been killed by God if their son, who may have been several months old or older, remained uncircumcised. She, no doubt, witnessed the hesitation of Moses to act and decided to take matters into her own hands. Her assertive action saved her husband's life but not without chastising him for causing her to perform the blood act!