Last year I received both the American opportunity credit and the Education nonrefundable credit; Why can I not receive both this year?

It depends. Per IRS: There are several differences and some similarities between the American Opportunity Tax Credit (AOTC) and the Lifetime Learning Credit (LLC).  You can claim these two benefits on the same return but not for the same student or the same qualified expenses. See "No Double Benefits Allowed" for more information on claiming one or more education benefits. 

You may have had a dependent or a spouse going to school too, or yourself at the same time.

@dsmithtax24

What you must likely received was the  American opportunity credit in two pieces. The non refundable portion 0n line 3 of Schedule 3 (then line 20 of form 1040) and the refundable portion on line 29 of form 1040.  See form 8863 for details.  

If you have no tax liability, this year, you will not receive the non refundable portion.