Because people reject God's guidance, they live lives that ultimately wreck other people and even themselves. God is basically employing the famous calculator mantra of "garbage in garbage out" -- partly to demonstrate for themselves that sin ruins lives. In particular, God "gave them over to a debased mind" (1:28). Basically the mind they chose for themselves.
The debased mind from rejecting God's guidance leads to a lot of sins and sinful attitudes that ruins lives, as listed below.
Sexual Immorality (1:29) -- examples include rape and incest
Wickedness, Maliciousness, and Evil-mindedness (1:29)
Covetousness and Envy (1:29) -- basically over-focusing on what you don't have
Murder (1:29)
Strife (1:29)
Deceit (1:29)
Backbiters (1:30)
Haters of God (1:30) -- note that God does not want to screw over people, and that is basically rejecting a guide to not screw over people
Violent (1:30)
Boastful pride (1:30)
Inventing evil things (1:30) -- there are a lot of sins not listed in the list
Disobeying parents (1:30) -- the Greek word for "disobeying" (Strong 545) conveys a sense of extreme disobedience, where there is far more focus on disobeying than obeying as well as having an unpersuaded attitude
Undiscerning (1:31) -- basically making bad choices
Untrustworthy (1:31)
Unloving (1:31)
Unforgiving (1:31)
Unmerciful (1:31)
Considering that there's the thing called "the righteous judgment of God" (1:32), doing these things wouldn't fare well in our record. In particular, doing such things results in being "deserving of death" (1:32). Because of sin, we lost the ability to live eternally on Earth on our own -- especially since sin separates us from God and God's powers of eternity. Not to mention that as sin stems from a sinful attitude and sin ruins lives, sinful attitudes have to be eventually taken out (because evil existing for eternity is not good!).
But even with awareness that such things are not good, unfortunately, many people (even us) do these things, some of which are habitual. Some people even "approve of those who practice [the sin]" (1:32), and we can see examples in corrupt people getting away without repercussions. The approval can indicate that having sinful desires takes priority.
So yeah, sin is definitely a big problem. But two chapters later, Paul will talk about how the problem can be dealt with.