I cannot understand why I am not getting credit for my child's college tuition when we qualify for the American Opportunity Tax Credit????

You may have answered one of the questions incorrectly in the Education section. 

Revisit that section and make sure that you have entered that you are at least a half time student, and that you haven't  taken the Hope or American Opportunity Credit for 4 previous years.

Qualifications for claiming the American Opportunity Tax Credit are:

• You paid qualified education expenses for higher education.
• You paid education expenses for eligible students.
• The eligible student is you, your spouse, or a dependent for whom you claim an exemption.
• Your modified adjusted gross income is $90,000 ($180,000 if married filing jointly) or less (The credit is reduced between $80,000 and $90,000 ($160,000 and $180,000).
• You must be taking courses at an eligible education institution, which is any college, university, or vocational school with a student aid program administered by the US Department of Education.