Data directory write privilege on different storage

I have two storageclass in my ocp.
I have a dynamic nfs storageclass and a local disk storageclass.
When I use the same deployment file with the same securityContext, I can write to the data dir on the NFS one but cannot touch on the local disk one. I have tried readOnlyRootFilesystem to false but still cannot get the local disk storageclass to be writeable but no such issue with my nfs one. So, what could I have been missing?