I will base this answer on the premise that an activity cannot be a reason to be excluded from the kingdom of God unless there is something sinful about it. This is a premise that it is reasonable to hold in light of verses such as:
Behold, the Lord's hand is not shortened, that it cannot save, or his ear dull, that it cannot hear; 2 but your iniquities have made a separation between you and your God, and your sins have hidden his face from you so that he does not hear. [Isaiah 59:1-2, ESV]
13 Let no one say when he is tempted, “I am being tempted by God,” for God cannot be tempted with evil, and he himself tempts no one. 14 But each person is tempted when he is lured and enticed by his own desire. 15 Then desire when it has conceived gives birth to sin, and sin when it is fully grown brings forth death. [James 1:13-15, ESV]
This leads us to the question: Why is habitual drunkenness a sin?
If we remember the definition of sin from passages such as Rom 3:20, Rom 7:7, Rom 7:13 and 1 John 3:4, sin essentially means to break God's law. So we should ask ourselves: what commandment is being broken when someone gets habitually drunk? I would say that such a person is breaking the commandment against idolatry:
Exodus 20:3-46 (ESV):
3 “You shall have no other gods before me.
4 “You shall not make for yourself a carved image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth. 5 You shall not bow down to them or serve them, for I the Lord your God am a jealous God, visiting the iniquity of the fathers on the children to the third and the fourth generation of those who hate me, 6 but showing steadfast love to thousands of those who love me and keep my commandments.
A habitual drunkard is someone who has made an idol out of alcohol. Such a person is devoting most their time to alcohol, using alcohol as an emotional crutch, as a way to cope with stress, to escape from daily life's problems, to distract themselves and have some fun, and many other similar reasons. And that's not even considering all the other well-known potential harmful side-effects to the person's own health and to their close ones (assuming that the drunkard lives under the same roof with other people).
Instead of finding comfort and joy and relief and everything that they need in God, a habitual drunkard has replaced God with their crutch: alcohol, and relegated God to a secondary plane. This is why I strongly believe this is a case of idolatry.
Instead, we should seek everything we need in God, through his Holy Spirit, as Ephesians 5:18-21 eloquently states:
18 And do not get drunk with wine, for that is debauchery, but be filled with the Spirit, 19 addressing one another in psalms and hymns and spiritual songs, singing and making melody to the Lord with your heart, 20 giving thanks always and for everything to God the Father in the name of our Lord Jesus Christ, 21 submitting to one another out of reverence for Christ. [Ephesians 5:18-21, ESV]
Romans 14:17 expresses a similar idea:
17 For the kingdom of God is not a matter of eating and drinking but of righteousness and peace and joy in the Holy Spirit. [Romans 14:17, ESV]
