Why are hard links not allowed for directories?

Directory hardlinks break the filesystem in multiple ways

They allow you to create loops

A hard link to a directory can link to a parent of itself, which creates a file system loop. For example, these commands could create a loop with the back link l:

mkdir -p /tmp/a/b
cd /tmp/a/b
ln -d /tmp/a l

A filesystem with a directory loop has infinite depth:

cd /tmp/a/b/l/b/l/b/l/b/l/b

Avoiding an infinite loop when traversing such a directory structure is somewhat difficult (though for example POSIX requires find to avoid this).

A file system with this kind of hard link is no longer a tree, because a tree must not, by definition, contain a loop.

They break the unambiguity of parent directories

With a filesystem loop, multiple parent directories exist:

cd /tmp/a/b
cd /tmp/a/b/l/b

In the first case, /tmp/a is the parent directory of /tmp/a/b.
In the second case, /tmp/a/b/l is the parent directory of /tmp/a/b/l/b, which is the same as /tmp/a/b.
So it has two parent directories.

They multiply files

Files are identified by paths, after resolving symlinks. So

/tmp/a/b/foo.txt
/tmp/a/b/l/b/foo.txt

are different files.
There are infinitely many further paths of the file. They are the same in terms of their inode number of course. But if you do not explicitly expect loops, there is no reason to check for that.

A directory hardlink can also point to a child directory, or a directory that is neither child nor parent of any depth. In this case, a file that is a child of the link would be replicated to two files, identified by two paths.

Your example

$ ln /Some/Direcoty /home/nischay/Hard-Directory
$ echo foo > /home/nischay/Hard-Directory/foobar.txt
$ diff -s /Some/Direcoty/foobar.txt /home/nischay/Hard-Directory/foobar.txt
$ echo bar >> /Some/Direcoty/foobar.txt
$ diff -s /Some/Direcoty/foobar.txt /home/nischay/Hard-Directory/foobar.txt
$ cat /Some/Direcoty/foobar.txt
foo
bar

How can soft links to directories work then?

A path that may contain softlinks and even soft linked directory loops is often used just to identify and open a file. It can be used as a normal, linear path.

But there are other situations, when paths are used to compare files. In this case, symbolic links in the path can be resolved first, converting it to a minimal, and commonly agreed upon representation creating a canonical path:

This is possible, because the soft links can all be expanded to paths without the link. After doing that with all soft links in a path, the remaining path is part of a tree, where a path is always unambiguous.

The command readlink can resolve a path to its canonical path:

$ readlink -f /some/symlinked/path

Soft links are different from what the filesystem uses

A soft link cannot cause all the trouble because it is different from the links inside the filesystem. It can be distinguished from hard links, and resolved to a path without symlinks if needed.
In some sense, adding symlinks does not alter the basic file system structure - it keeps it, but adds more structure like an application layer.

From man readlink:

 NAME
        readlink - print resolved symbolic links or canonical
        file names

 SYNOPSIS
        readlink [OPTION]... FILE...

 DESCRIPTION
        Print value of a symbolic link or canonical file name

        -f, --canonicalize
               canonicalize by  following  every  symlink  in
               every component of the given name recursively;
               all but the last component must exist
        [  ...  ]

"You generally should not use hard links anyway" is over-broad. You need to understand the difference between hard links and symlinks, and use each as appropriate. Each comes with its own set of advantages and disadvantages:

Symlinks can:

• Point to directories
• Point to non-existent objects
• Point to files and directories outside the same filesystem

Hard links can:

• Keep the file that they reference from being deleted

Hard links are especially useful in performing "copy on write" applications. They allow you to keep a backup copy of a directory structure, while only using space for the files that change between two versions. Note that the implementation must first break the link (or modifications will apply to the original file, too!).

The command cp -al is especially useful in this regard. It makes a complete copy of a directory structure, where all the files are represented by hard links to the original files. You can then proceed to update files in the structure (after creating actual copies of only these files), and only the files that you update will take up additional space. This is especially useful when maintaining multigenerational backups.