The search parameter 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!
