This is not the place to go into Greek mythology in any depth, but I do not have to. Greek mythology deals with the stories of their gods. Certainly, there is a fascinating aspect to the stories surrounding the Greek gods. There is probably nothing wrong with an elementary knowledge of some of these stories. Some of them are a part of our Western culture and its common stock of knowledge. An example of this would be the story of Icarus who was killed when he flew too near the sun with the wings made for him by his father because the wax joints of his wings melted and he fell into the sea. This story has been used as an anology for many things and knowing it is important for following the reasoning of some.
However, there is a great danger as well. I would be curious to know how this teen became so interested in Greek mythology. I noticed a number of years ago that more and more of the cartoons for children invoked memories of these ancient gods and goddesses. We have seen the same thing in television and movies. More recently, many computer games operate within the framework of the false gods. A fascination with Greek mythology comes from somewhere. I would think that it probably comes from one of these sources or a similar one.
This brings up an interesting question. Why does a culture that is so antigonistic to God spend so much energy reviving interest in the gods? We must remember that the gods were not just good stories to the ancient peoples. They were their gods. They served them and prayed to them. They sacrificed children to them and built temples to them. They were not just play-toys of the imagination. They had power over the people. We are foolish to think that we have changed or evolved in such a way that these gods can no longer have any power over us.
As such, the Bible continually warned against the false gods. The first of the Ten Commandments states, "Thou shalt have no other gods before me" (Exodus 20:3). The Israelites are also told, "Ye shall not go after other gods, of the gods of the people which are round about you" (Deuteronomy 6:14). God refers to the gods of the nations (and that would include the gods of Greece) as idols (1 Chronicles 16:26; Psalm 96:5). They were designed to be worshipped and served. In Jeremiah 2:28, Judah is condemned because they had multiplied gods according to the number of their cities. There is only one God. There is no room for other gods.
In addition to all this, the gods are connected to devils (often called demons today). Deuteronomy 32:17 states, "They sacrificed unto devils, not to God; to gods whom they knew not, to new gods that came newly up, whom your fathers feared not." The gods are devils. Evidently, there are real living devils who serve in the place of many of the gods. As idols of stone or brass, the gods are helpless. However, in their connection with devils, they are most dangerous. That is, a fascination with the gods is an important gateway into devil-worship. Other verses bear this out as well. Leviticus 17:7 speaks of offering sacrifices to devils. Paul declared, "But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils" (1 Corinthians 10:20). Connection with these gods is equated with a fellowship with devils. This is very serious indeed.
Finally, the Bible prophesies that the last days will be characterized by a revival of demonic influences. 1 Timothy 4:1 states, "Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils." The time of the tribulation will be a tme when men will "worship devils, and idols of gold, and silver, and brass, and stone, and of wood' (Revelation 9:20). We see here the connection between the false gods and the worship of devils.
Believers are warned of unequal yokes with unbelievers in 2 Corinthians 6:14-17. Paul specifically asks (v.16), "And what agreement hath the temple of God with idols?" I would ask the same thing. What connection can a believer in the true and only God have with false gods and the devils they represent? We should beware of such things. We can know about them, but we should not allow ourselves to be strongly drawn to them. Their influence is more powerful than most would recognize. 2 Corinthian 6:17 concludes the section on unequal yokes with this injunction: "Wherefore come out from among them, and be ye separate, saith the Lord, and touch not the unclean thing; and I will receive you." We would do well to do the same.