We all sin, and, as St. Paul admits, we keep doing it. However, notice how he wisely writes: “that which I hate, I keep doing.” As long as you “hate” sin, that is, your will is not to sin, then you are not attached to it.
The issue, I think, is that the splendor of a plenary indulgence cannot be granted to someone who is detached only from the most grave sins - the ones of the Decalogue. One must also be detached from venial sin. For instance, I understand this as desiring to never willfully offend God, and not being attached to anything that could offend Him.