PHP strange If Else loop output if i make exact opposite of current condition

what i am trying to do check the $_GET['mode'] for specific page types, if mode is favorites , rss or my_uploads page then dont show the RSS link like this

<?php
$mode = $_GET['mode'];
if($mode == 'favorites' || $mode == 'rss' || $mode == 'my_uploads'){
$RSS_link = null;
}else{
$RSS_link = create rss link logic here ;
}

then later showing the link to RSS FEED only if the link is created like this

<?=(isset($RSS_link)) ? '<a href="'.$RSS_link.'">RSS FEED</a>' : '' ;?>

the above code is working fine, and shows the RSS FEED Link only when pages are not favorites, rss,my_uploads

but if change the RSS creating condition like this.

<?php

    if($mode != 'favorites' || $mode != 'rss' || $mode != 'my_uploads'){
    $RSS_link = create rss link logic here ;
    }else{
    $RSS_link = null;
    }

i.e. just changing the operators to opposite and moving if to else and else to if,

<?=(isset($RSS_link)) ? '<a href="'.$RSS_link.'">RSS FEED</a>' : '' ;?>

and then try to show the RSS FEED Link , it shows the link, no matter what the mode is set.

Why is this happening? How can i fix this ?