It is either a subreddit that is very sensitive or the Mod is the sensitive one, and that is why you have to take caution when you want to join a private subreddits.
Private subreddits are not like any other Reddit community. The environment is different and their rules are often more critical. They are made in the subreddit settings to protect the interest of the moderators, members, and the execution of these rules starts from the very point someone mails an application for membership to a Moderator.
See also: How do you “tag” users on Reddit posts
What you should know
Before you join a private subreddit, it is very important to go through rules or ask questions on Reddit’s FAQ page. This will guide you so that you don’t get bounced out a few days after being approved: I believe staying should be as important as joining.
If the private subreddit you wish to join is on the list of r/top/ (the top list), then your Reddit Karma (the score you get for posting and commenting on Reddit) must be on the top 1%.
Steps to getting approved
Step 1: Go to www.reddit.com, login, or Sign up to Reddit: Login with your username and password.
If you are not a member yet, you can sign up for a Reddit account by typing in your email, then type in a password and username that is strong enough to match the standard required of Reddit and click sign up. This generates a Reddit account immediately. Visit your mail; click the link to confirm your account.
Step 2: Hover your cursor key to click the envelope icon on the top right side of the horizontal menu bar to open up the page where you will see and click the “send a message” option on the blue menu bar.
Step 3: In the receiver’s box (: TO), type in the name of the subreddit (typed as /r/name) you are interested in. This will help send messages to all moderators of the named subreddit.
If you don’t know the name of the subreddits, you can find it by searching for www.reddit.com/subreddits/ on a search engine. Once the page opens, you will see the /r/name of several communities listed. You can type in a keyword of any community of interest in the search box. For instance, if I am interested in “books”, I would have to type it “in” to find several book-related subreddits or communities. You can copy and paste the /r/name in the receiver’s box.
You can also open a private subreddit in your browser to find the /r/name at the end of the URL.
Step 4: Type in a precise subject in the subject box.
Step 5: For the message box, compose a brief convincing private message explaining why you wish to join the community. The first line should be a brief introduction of you, while the second line should be a good reason why you wish to join the community.
After that, give well-known requirements that most private communities require of prospective members, relate it with well-known rules of the community, and affirm a commitment to abide by them. Then, end it with a brief summary, and click the send button to forward your message.
PS: Applying to a subreddit does not mean that you will be approved. But writing a good subject line and message will give you a better chance to be accepted. You can go to reddit.com/r/help/ or search for Reddit FAQ. There you can ask questions on how to join a private subreddit.