PHP - Certain array indexes not accepting variables

I have a bizarre issue that I cannot for the life of me seem to resolve.

I am generating an array ($tags) from a mysql query, it looks something like this:

Array(
    [1] => Safety Toe
    [2] => Waterproof
)

Then I have another array ($link) I generate in a loop:

Array(
    [1] => Array(
        [0] => 1
        [1] => 2
    )
    [2] => Array(
        [0] => 1
        [1] => 2
    )
)

Also, I have 2 predefined variables that in this case are as follows:

$max == 2;
$title_count == 3;

Later on I have 2 for loops, 1 is nested:

for($y=0;$y<$max;$y++){
    for($x=1;$x<=$title_count;$x++){
        if($x==1){
            echo "<tr><td>".$tags[$link[$x][$y]]."</td>";
        }elseif($x<$title_count){
            echo "<td>".$tags[$link[$x][$y]]."</td>";
        }else{
            echo "<td>".$tags[$link[$x][$y]]."</td></tr>";
        }
    }
}

This should produce something along the lines of:

Safety Toe Safety Toe Safety Toe
Waterproof Waterproof Waterproof

The problem is this is what I get:

Safety Toe Safety Toe Safety Toe 

This made me curious, so I tried manually inputting $tags[2]. That worked and produced:

Waterproof Waterproof Waterproof
Waterproof Waterproof Waterproof

However, if I manually set them all to $tags[$link[1][1]] ($link[1][1] == 2) I get an empty result. If I set a variable, such as $test = $link[1][1]; (which echoes as 2), and then try $tags[$test], I get nothing. However if I set $test = 2; and do $tags[$test] I get Waterproof.

I am beyond bewildered here, if there is anything I'm missing, or any ideas as to why this would be the way it is, please let me know.

Thanks!