As Mover mentioned, could be your CV? Perhaps you are applying for a position higher than what they are expecting for someone of your background? Most consultancies that I have visited DO prefer people from industry, but it is a very competitive environment which you have prove to them why they should recruit you over someone else, for example. Perhaps you need to forget Consulting as either you are not calibre they require (period) or that you need to work on something substantial to prove your worth. I hope you consider the latter and reapply in a few years time.