Daniel 10 begins by telling us that the prophet had been fasting and mourning for three full weeks (verses 1 - 3). He then sees, near the river Hiddekel, a vision of one of God's righteous angels. The angelic being states that God sent him the moment Daniel began to humble himself and pray for understanding (verse 12). Did you catch that? The spirit being (who was very likely the archangel Gabriel, see 8:16 and 9:21), traveling in the spirit realm, took a FEW WEEKS to reach the prophet from God's throne! What would cause such an unusual delay for one of the most powerful angels ever created?
Gabriel, who normally would have delivered God's message the moment after he got it, was UNABLE, of himself, to get past the 'prince of the kingdom of Persia!' It took the power of another one of God's holy angels, Michael (the only other Archangel the Bible mentions), to come and help him fight his way through to deliver his message.
Since Gabriel was sent directly by God, whoever hindered him from completing his mission was almost certainly an enemy of righteousness. Could the evil "prince of the kingdom of Persia" (10:13), who almost stopped Gabriel's journey, be a powerful human being? The short answer is NO. Human beings have no power, of themselves, to fight even the weakest of spirit beings (Hebrews 1:7). A small group of the lowest of angels could kill COUNTLESS human beings at will. Flesh and blood beings are completely helpless before the power of spirit-composed beings (Mark 16:17, Luke 9:1).
When God wanted to rescue Jerusalem from being attacked by Sennacherib, he needed only ONE angel to kill 185,000 Assyrian warriors in a single night (Isaiah 37:36). This means that while a human prince could not have resisted a holy angel, it must have been a spirit who was evil and willing to fight a righteous and powerful being making his way to Daniel.
One of the literary techniques the Bible uses is symbolism. The use of a reference like 'the prince of the kingdom of Persia' to symbolically represent a powerful, demonic spirit being is found elsewhere in scripture (see Ezekiel 28:12 - 19, Isaiah 14:4, 12 - 15). Although nominally these texts appear addressed to mere human kings, they are actually about a powerful, ambitious, and blindly vain spirit - the ruler over all the rebellious angels. No ordinary human king, for example, could have been in the Garden of Eden (compare Genesis 3:22 - 24 to Ezekiel 28:13).
Gabriel did not say just anyone fought him to try to stop his message from reaching Daniel. The evil spirit who opposed him is the "prince" of PERSIA and not Babylon or some other nation. God seems to have assigned angels different principalities and powers (see Romans 8:38, Ephesians 3:10, Colossians 1:16, 2:15). For example, the archangel Michael is called a prince of Israel (Daniel 10:21) and a chief prince (verse 13). Gabriel and Michael were possibly assigned authority over the affairs for the nation Israel. In like fashion, the devil has assigned certain demons to positions of authority over earthly kingdoms (Ephesians 6:12), such as a powerful evil spirit assigned to Persia.
What happened to Gabriel was that when he got near Persia he met with resistance from, and no doubt had to fight, an evil angel (with lesser demonic powers under his control?) given authority to influence the affairs of the world power. After an unsuccessful 21-day attempt to overcome the demon controlling access to Persia, Michael came and helped Gabriel 'break through' to deliver his message. One wonders how many angels fight on a daily basis over who has authority to influence different parts of the human race!