So, you want to highlight row 4, since that is the only row where not all three values match. Cat and dog are also in rows 1 and 5, but in these, the value in column C is the same.
You could use this formula in D1 and copy down:
=IF(OR(AND(SUMPRODUCT(--($A$1:$A$7&$B$1:$B$7=A1&B1))=2,SUMPRODUCT(--($A$1:$A$7&$B$1:$B$7=A1&B1),--($C$1:$C$7<>C1))>0),SUMPRODUCT(--($A$1:$A$7&$B$1:$B$7=A1&B1),--($C$1:$C$7<>C1))>1),"here","")
(It's not an array formula).
Or use Conditional Formatting on the cells C1:C7
The formula is
=OR(AND(SUMPRODUCT(--($A$1:$A$7&$B$1:$B$7=A1&B1))=2,SUMPRODUCT(--($A$1:$A$7&$B$1:$B$7=A1&B1),--($C$1:$C$7<>C1))>0),SUMPRODUCT(--($A$1:$A$7&$B$1:$B$7=A1&B1),--($C$1:$C$7<>C1))>1)
I added a case where A and B are the same in only two rows and C is different for these two rows. These two should be highlighted as far as I understand the task.