The seven deadly sins are all things that have a serious negative impact on you and your life if you give into them too much. They’re all very general habits/feelings/desires that most people feel/experience which can lead you to hurt yourself and/or others, and haste/impatience checks both those boxes.
And I suppose as “sins” they’re supposed to lead you to do “un-Christian” things, but impatience probably does that more than sloth, right? Like you’re much more likely to hurt yourself and/or others if you do things fast without thinking than you are by just sitting and doing nothing all day.
I guess all of the sins are also all some form of carelessness too which also applies to being hasty or impatient.
Sloth is another word for neglect.
And sustained neglect can do terrible things.
Think a parent watching TV or playing with their phone and their child suffering from their inaction.
“I’ll do it tomorrow” can have huge repercussions when the thing needing tending is important.