Question

access(2) man page says,

CAVEAT
Access() is a potential security hole and should never be used.

But what is the security hole and why I should not use it?

Answer 1

Linux Man pages clearly describes it

Warning: Using access() to check if a user is authorized to, for example, open
a file before actually doing so using open(2) creates a security hole, because
the user might exploit the short time interval between checking and opening
the file to manipulate it. For this reason, the use of this system call
should be avoided.

Also note. For security reason security exploits are not easily reachable to public.