Rejecting people without offending them seems to be an important social skill, and probably one that most people only acquire through effort and experience. There are countless situations in life in which it is necessary to reject a person’s offer or request: they may not be the best candidate for a job, you may not have time to attend their party on a particular day, you may not want to help them out with a project, etc. Unless you get very few requests or have a lot of free time, you are going to have to say ‘no’ to something.
I have experience with people who manage this process terribly. For instance, those who send no response and ignore you, leaving you uncertain about what they think and why. There are those who are unnecessarily personal and hostile in rejections, and those who are unnecessarily deferential and euphemistic. Ideally, you want to pass along the message clearly, without malice, while indicating a willingness to consider other potential offers in the future. I have seen a few cases of people doing this really well, and think of those as models to follow.