Thats wrong. You can put all your work under any permissible license and use any GPL library. The same is true for anyone who get the work from you. No need to

Thats wrong. You can put all your work under any permissible license and use any GPL library. The same is true for anyone who get the work from you. No need to re-license anything. Large programs often use multiple different software licenses without having to relicensing everything to be the same. They just have to be compatible.