The [search parameter][1] will help you do this really elegantly.

In the code below I've called the category field `categoryField`, but you'll have to swap that to suit your site.

    {# Get current students (students who aren't also in the alumni category) #}
    {% set currentStudents = craft.entries.section('people').search('categoryField:student -categoryField:alumni') %}
    
    {% for student in currentStudents %}
    	{# Output your students here #}
    {% endfor %}

This is basically asking Craft to respond with the entries that have the categoryField including student but not (indicated by the `-` before) including alumni.

You could probably also streamline the other bits of your code using this method.

I've tested this as working on Craft 2.5.2757

Hope that helps!


  [1]: https://craftcms.com/docs/templating/craft.entries#search