Why is nth-child selector not working?

Try this!

<div id="social-links">
  <a href=""><div class="social-logo"></div></a>
  <a href=""><div class="social-logo"></div></a>
  <a href=""><div class="social-logo"></div></a>
  <a href=""><div class="social-logo"></div></a>
</div>

CSS

.social-logo {
    display: inline-block;
    width: 24px;
    height: 24px;
    transition: background-image .2s;
}

#social-links a:nth-child(1) .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-linkedin.svg');
}

#social-links a:nth-child(1):hover .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-linkedin-copy.svg');
}

#social-links a:nth-child(2) .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-dribbble.svg');
}

#social-links a:nth-child(2):hover .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-dribbble-copy.svg');
}

#social-links a:nth-child(3) .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-email.svg');
}

#social-links a:nth-child(3):hover .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-email-copy.svg');
}

#social-links a:nth-child(4) .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-insta.svg');
}

#social-links a:nth-child(4):hover .social-logo {
    background-image: url('https://mysql-raigovind93.c9users.io/Cally%20Dai//img/footer/logo-insta-copy.svg');
}

Demo live - https://jsfiddle.net/g59wa8uf/

The nth-child selector counts siblings (i.e., elements having the same parent).

In your HTML structure, div.social-logo is always the first, last and only child of a. So nth-child has only one element to count.

However, there are multiple anchor elements, all of which are siblings (children of #social-links), so nth-child can target each one.

#social-links a:nth-child(1) div 
#social-links a:nth-child(2) div 
#social-links a:nth-child(3) div 
              .
              .
              .

Add space before ':' example:-

tr :nth-child(2)
{
    text-align: right;
}