Jesus is not saying that the cares of this life and riches are intrinsically evil; they are neutral. However, involvement in or pursuit of them may be easily overdone and cause great spiritual loss. He is warning people with too many interests. The most important interests, the spiritual ones, almost invariably get crowded out.
Even a person heavily involved in charitable works may be misusing time (Luke 10:40-42). Another may be so intent on his business that he is too tired to study or pray effectively, or for that matter, to think of anything else. Such a person—one who should heed Jesus' warning—has allowed other things to control his life.
In many cases, our worst enemies are not the obviously bad things, but the necessary and even the good things which we allow to be overdone. In athletics, is not the second best athlete always the strongest enemy of the first? So it is in prioritizing. Much of the time, our chief problem is a lack of commitment to the highest priority; we allow the secondary priorities to steal time from the primary one.
Consider the man in the parable of Luke 12:20-21:
But God said to him, "You fool! This night your soul will be required of you; then whose will those things be which you have provided?" So is he who lays up treasure for himself, and is not rich toward God.
He was a fool because he did not have enough understanding and character to know when enough is enough. In his lust for more, he burned up his time on lower priority concerns and neglected building character.