Why do inode numbers start from 1 and not 0?

0 is used as a sentinel value to indicate null or no inode. similar to how pointers can be NULL in C. without a sentinel, you'd need an extra bit to test if an inode in a struct was set or not.

more info here:

All block and inode addresses start at 1. The first block on the disk is block 1. 0 is used to indicate no block. (Sparse files can have these inside them)

http://uranus.chrysocome.net/explore2fs/es2fs.htm

for instance, in old filesystems where directories were represented as a fixed array of file entries, deleting a file would result in setting that entry's inode val to 0. when traversing the directory, any entry with an inode of 0 would be ignored.

Usually, the inode 0 is reserved because a return value of 0 usually signals an error. Multiple method in the Linux kernel -- especially in the VFS layer shared by all file systems -- return an ino_t, e.g. find_inode_number.

There are more reserved inode numbers. For example in ext2:

#define EXT2_BAD_INO             1      /* Bad blocks inode */
#define EXT2_ROOT_INO            2      /* Root inode */
#define EXT2_BOOT_LOADER_INO     5      /* Boot loader inode */
#define EXT2_UNDEL_DIR_INO       6      /* Undelete directory inode */

and ext3 has:

#define EXT3_BAD_INO             1      /* Bad blocks inode */
#define EXT3_ROOT_INO            2      /* Root inode */
#define EXT3_BOOT_LOADER_INO     5      /* Boot loader inode */
#define EXT3_UNDEL_DIR_INO       6      /* Undelete directory inode */
#define EXT3_RESIZE_INO          7      /* Reserved group descriptors inode */
#define EXT3_JOURNAL_INO         8      /* Journal inode */

and ext4 has:

#define EXT4_BAD_INO             1      /* Bad blocks inode */
#define EXT4_ROOT_INO            2      /* Root inode */
#define EXT4_USR_QUOTA_INO       3      /* User quota inode */
#define EXT4_GRP_QUOTA_INO       4      /* Group quota inode */
#define EXT4_BOOT_LOADER_INO     5      /* Boot loader inode */
#define EXT4_UNDEL_DIR_INO       6      /* Undelete directory inode */
#define EXT4_RESIZE_INO          7      /* Reserved group descriptors inode */
#define EXT4_JOURNAL_INO         8      /* Journal inode */

Other fileystems use the ino 1 as root inode number. In general, a file system is free to choose its inode numbers and its reserved ino values (with the exception of 0).