This won't soothe the pain of feeling rejected but I think it can help the suffering to accept that sites have to sort from many applications of well-qualified applicants with congruent goals and based only on paper (not you in person) they have to choose a pragmatically limited number to interview, based on their best guess of "fit" and the likelihood that you would match with them. Just as you are trying to "read" the site, they are trying to "read" the application and it can be true that you have qualifications that are outstanding--but may not "fit". (eg: lots of research experience, your advisor raves about your research skills but the site knows they can offer little in this area--they may not invite you because they view you as over-qualified and likely to want a place to use those skills...) I know it seems like a Catch-22; it is a complex, unwieldy process. AND most candidates find their place and often are very happy at a place they did not see, at this stage, as their destiny. It is very hard to trust the process...but it is what we have and works better than what used to be.
