Laravel 5 custom helper could not set session

I have custom helper, class, in my Laravel project:

<?php

namespace App\Http\Helpers;

class FoxUtils {

  public static function isAuthTo($name)
  {
     if (self::test($name)){
       \Session::push('AuthList',[$name => true]);
       return true;
     }
     else{
      \Session::push('AuthList',[$name => false]);
       return false;
     }
  }
}

There two notes:

The session variable AuthList is numerical indexed array with values as arrays like the following:

array:2 [▼
  0 => array:1 [▼
    "name1" => true
  ]
  1 => array:1 [▼
    "newName" => true
  ]
]

The value "name1" => true is defined from other place than my helper. When I try to use my helper's method I respect new keys should be added to the array:

\FoxUtils::isAuthTo('AnotherName');
dd(session('AuthList'))

the above code prints array with only two keys while I expect three:

array:2 [▼
      0 => array:1 [▼
        "name1" => true
      ]
      1 => array:1 [▼
        "AnotherName" => true
      ]
    ]

In other words, always the last value of the AuthList is replaced with new value! What is the problem here?

via Chebli Mohamed