When I say something that is hard to hear I say it in a complex way. As if saying it in a hard to understand way will soften the blow. But it just muddies the message and causes confusion.
Instead of saying "I don't want the soup", I say something like "It's not that I don't like your soup; I just don't feel like it right now. I mean it's not my favourite soup and I wouldn't be unhappy having it." In response I'll just get a confused stare. I still have to deliver the hurtful message that I don't like the soup, and often have to explain what I meant in more detail. It takes courage to be direct, but delivers the painful message swiftly and concisely and we can move on from there.
Describing what something is not is a more moderate way of saying something in English, however it's often more confusing than helpful. A typical response to "How's it going" is "Not bad", which is positive, but not as positive as "good". Negations put a statement between the extreme polarities; saying "it's not that I don't like your soup" I'm stating that I don't not like the soup, which is a weaker statement than that I like the soup. This is a peculiarly English thing; in Slavic languages more negations just emphasises the no more strongly, there's no notion of a double negative. The Slavic way is easier to understand (and incidentally their spelling is logical, unlike English, too).
I was recently reading A Founder's Guide to Writing Well which emphasised the standard rule of using short, simple words. If you want to be understood you should make your writing and speech as easy to interpret as possible. I'm going to strive to be more direct and simple to be more easily understood, and show respect to my audience.