1) Lowering your average age of accounts. All else equal, if you have 2 credit cards open, one that you've had for 8 years and one that you've had for 6 years, the average age would obviously be 7. If you proceed to open a dozen airline cards in one year (regardless of whether you close them or not), your average age would plummet and could negatively impact your score.
2) Each time you apply for credit or a loan, a "hard inquiry" shows up on your credit report and can negatively impact your score. The scoring system is designed to account for multiple inquiries in a short period of time to allow people to shop around for a mortgage or auto loan by grouping them as one inquiry (as long as they are done in a 30-45 day period). This is not the case for credit or store card applications.
3) In addition to simply applying for credit, having numerous recently open accounts and newly available credit is also perceived as a risk and can lower your score.
The above being said, you may or may not experience a significant hit on your score through "churning." Don't assume that because someone else did it without any negative impacts that the same will be true for you. If you will be applying for a mortgage in the near future, I would advise against it. For everyone else, YMMV.